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we 've already taken definite integrals and we 've seen how they represent or denote the area under a function between two points and above the x axis . but let 's do something interesting . let 's think about a definite integral of f of x dx , it 's the area under the curve , f of x , but instead of it being mean bet... | let 's think about a definite integral of f of x dx , it 's the area under the curve , f of x , but instead of it being mean between two different x values , say a and b like we see in multiple times , let 's say it 's between the same one . let 's say it 's between c and c. let 's say c is right over here . what do yo... | it is understandable that the resultant area = 0 , but if i say that an integral is the anti-derivative , whereas the function being integrated is the anti-derivative , should n't that c signify a portion of the original function ? |
we 've already taken definite integrals and we 've seen how they represent or denote the area under a function between two points and above the x axis . but let 's do something interesting . let 's think about a definite integral of f of x dx , it 's the area under the curve , f of x , but instead of it being mean bet... | well there is no width , we 're just at a single point . we 're not going from c to c plus some delta x or c plus some even very small change in x or c plus some other very small a value . we 're just , saying at the point c. when we 're thinking about area we 're thinking about how much two-dimensional space you 're t... | what is the difference between f ( c ) and the definite integral from c to c of f ( x ) dx ? |
we 've already taken definite integrals and we 've seen how they represent or denote the area under a function between two points and above the x axis . but let 's do something interesting . let 's think about a definite integral of f of x dx , it 's the area under the curve , f of x , but instead of it being mean bet... | let 's think about a definite integral of f of x dx , it 's the area under the curve , f of x , but instead of it being mean between two different x values , say a and b like we see in multiple times , let 's say it 's between the same one . let 's say it 's between c and c. let 's say c is right over here . what do yo... | for example , the definite integral from c to c of 2x dx is 0 , but f ( c ) is c^2 ? |
we 've already taken definite integrals and we 've seen how they represent or denote the area under a function between two points and above the x axis . but let 's do something interesting . let 's think about a definite integral of f of x dx , it 's the area under the curve , f of x , but instead of it being mean bet... | but let 's do something interesting . let 's think about a definite integral of f of x dx , it 's the area under the curve , f of x , but instead of it being mean between two different x values , say a and b like we see in multiple times , let 's say it 's between the same one . let 's say it 's between c and c. let 's... | what is the difference in meanings of the two , like the definite integral is supposed to represent the total change in x over the interval , but what does f ( c ) mean ? |
we 've already taken definite integrals and we 've seen how they represent or denote the area under a function between two points and above the x axis . but let 's do something interesting . let 's think about a definite integral of f of x dx , it 's the area under the curve , f of x , but instead of it being mean bet... | the height here is f of c. what 's the width ? well there is no width , we 're just at a single point . we 're not going from c to c plus some delta x or c plus some even very small change in x or c plus some other very small a value . | if we gon na add every integrals over a single point ( from a to b ) what 's we gon na have ? |
we 've already taken definite integrals and we 've seen how they represent or denote the area under a function between two points and above the x axis . but let 's do something interesting . let 's think about a definite integral of f of x dx , it 's the area under the curve , f of x , but instead of it being mean bet... | i encourage you to pause the video and try to think about it . well if you try to visualize it , you 're thinking , well the area under the curve f of x , above the x axis , from x equals c to x equals c. so this region , i guess we could call it , that we think about it , does have a height . the height here is f of c... | if the area on the same point is 0 , then reinmann sum wo n't work as it slices the region below the graph into infinitesimally small segments as the change in x approaches zero ... .can someone please explain why it works ? |
we 've already taken definite integrals and we 've seen how they represent or denote the area under a function between two points and above the x axis . but let 's do something interesting . let 's think about a definite integral of f of x dx , it 's the area under the curve , f of x , but instead of it being mean bet... | well if you try to visualize it , you 're thinking , well the area under the curve f of x , above the x axis , from x equals c to x equals c. so this region , i guess we could call it , that we think about it , does have a height . the height here is f of c. what 's the width ? well there is no width , we 're just at a... | how come the width be 0 ? |
we 've already taken definite integrals and we 've seen how they represent or denote the area under a function between two points and above the x axis . but let 's do something interesting . let 's think about a definite integral of f of x dx , it 's the area under the curve , f of x , but instead of it being mean bet... | we 've already taken definite integrals and we 've seen how they represent or denote the area under a function between two points and above the x axis . but let 's do something interesting . | if we were to break the function up into individual points ( tiny rectangles where the base is effectively zero ) , would the sum of all the integrals at these points add up to zero and therefore the integral of any function would result in a value of zero ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | and you 've probably shown for yourselves that you can do it in either way . you could have some matrix times an identity matrix and get that matrix again . now if matrix a right over here is a square matrix , then in either situation , this identity matrix is going to be the same identity matrix . but if matrix a is n... | so the zero matrix is not unique , right ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | and you 've probably shown for yourselves that you can do it in either way . you could have some matrix times an identity matrix and get that matrix again . now if matrix a right over here is a square matrix , then in either situation , this identity matrix is going to be the same identity matrix . | for a given matrix a with format nxm , does the zero matrix for a needs to be strictly a mxn matrix filled with zeros ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | 0 times 1 plus 0 times 3 is going to be 0 . you keep going , 0,0,0,0 . if we had a - just to make the point clear - let 's say we had a matrix 1,2,3,4,5,6 . | i think the answer is yes , so it can satisfy 0 x a = a x 0 = 0 but what about a matrix that satisfies 0 x a = 0 but do not satisfies a x 0 = 0 ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | and you 've probably shown for yourselves that you can do it in either way . you could have some matrix times an identity matrix and get that matrix again . now if matrix a right over here is a square matrix , then in either situation , this identity matrix is going to be the same identity matrix . | is it really true that any matrix ( first ) times an identity matrix ( second ) equals the first matrix ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | and you 've probably shown for yourselves that you can do it in either way . you could have some matrix times an identity matrix and get that matrix again . now if matrix a right over here is a square matrix , then in either situation , this identity matrix is going to be the same identity matrix . | btw ... ... .. is `` zero '' matrix and `` null '' matrix the same thing ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | and you 've probably shown for yourselves that you can do it in either way . you could have some matrix times an identity matrix and get that matrix again . now if matrix a right over here is a square matrix , then in either situation , this identity matrix is going to be the same identity matrix . but if matrix a is n... | what is the dimension if we multiply 5x2 zero matrix with 2x3 non zero matrix what is going to be the dimension of the new matrix is it going to be 5x3 idk ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | and you 've probably shown for yourselves that you can do it in either way . you could have some matrix times an identity matrix and get that matrix again . now if matrix a right over here is a square matrix , then in either situation , this identity matrix is going to be the same identity matrix . but if matrix a is n... | is there any reason why a zero matrix would n't always be a square matrix like the identity matrix is ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | so , we know that 0 times anything is equal to 0 . or , anything times 0 is equal to 0 . so what would be the analogy if we 're thinking about matrix multiplication ? well , it would be some matrix that if i were to multiply it times another matrix , i get , i guess you could say that same 0 matrix again . | if the two matrixes are not defined , would they still equal zero ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | and you 've probably shown for yourselves that you can do it in either way . you could have some matrix times an identity matrix and get that matrix again . now if matrix a right over here is a square matrix , then in either situation , this identity matrix is going to be the same identity matrix . | now my question is , cant the zero matrix have its dimensions as nx2 ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | and you 've probably shown for yourselves that you can do it in either way . you could have some matrix times an identity matrix and get that matrix again . now if matrix a right over here is a square matrix , then in either situation , this identity matrix is going to be the same identity matrix . | is a zero matrix that is 3x2 the same as a zero matrix that is 4x4 ( or of any size ) ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | and you 've probably shown for yourselves that you can do it in either way . you could have some matrix times an identity matrix and get that matrix again . now if matrix a right over here is a square matrix , then in either situation , this identity matrix is going to be the same identity matrix . | can there be a non-zero matrix ( c ) where a x c = o ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | it depends what the dimensions of a are going to be , but you could image what a 0 matrix might look like . for example , if a is 1,2,3,4 , what 's a 0 matrix that i could multiply this by to get another 0 matrix ? well , it might be pretty straight forward , if you just had a ton of zeros here , when you multiply this... | is a 3 by 3 zero matrix equivalent to a 2 by 2 zero matrix ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | and you 've probably shown for yourselves that you can do it in either way . you could have some matrix times an identity matrix and get that matrix again . now if matrix a right over here is a square matrix , then in either situation , this identity matrix is going to be the same identity matrix . | is the zero matrix over here the same as the zero matrix we learned during addition and subtraction of matrices ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | and you 've probably shown for yourselves that you can do it in either way . you could have some matrix times an identity matrix and get that matrix again . now if matrix a right over here is a square matrix , then in either situation , this identity matrix is going to be the same identity matrix . | if we have a axb zero matrix and a bxc matrix , would the dimensions of the product of the two matrices axc , in general ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | now if matrix a right over here is a square matrix , then in either situation , this identity matrix is going to be the same identity matrix . but if matrix a is not a square matrix , then these are going to be two different identity matrices , depending on the appropriate dimensions . now , let 's see if we can extend... | are all matrices of the same dimensions an identity matrix for zero matrices ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | 0 times 1 plus 0 times 3 is going to be 0 . you keep going , 0,0,0,0 . if we had a - just to make the point clear - let 's say we had a matrix 1,2,3,4,5,6 . | is ' [ 0 0 0 ] * [ 2 5 9 ] ' ' [ 0 0 0 ] * [ 1 2 3 ] ' defined ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | and you 've probably shown for yourselves that you can do it in either way . you could have some matrix times an identity matrix and get that matrix again . now if matrix a right over here is a square matrix , then in either situation , this identity matrix is going to be the same identity matrix . | zero matrix dimension depend on the matrix a. ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | and you could view 1 as essentially the identity . the identity number , or this is the identity property of multiplication . you multiply 1 times any number , you get that number again . | o.a=a.o=o this is identity property so i call zero matrix is same thing in identity martix ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | so , we know that 0 times anything is equal to 0 . or , anything times 0 is equal to 0 . so what would be the analogy if we 're thinking about matrix multiplication ? | is n't ab not equal to ba ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | and you 've probably shown for yourselves that you can do it in either way . you could have some matrix times an identity matrix and get that matrix again . now if matrix a right over here is a square matrix , then in either situation , this identity matrix is going to be the same identity matrix . but if matrix a is n... | a zero matrix is just a matrix with 0 as the entries , right ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | if we had a - just to make the point clear - let 's say we had a matrix 1,2,3,4,5,6 . so over here , we want to multiply this times - let 's see , in order for the matrix multiplication to work , my 0 matrix has got to have the same number of columns as this one has rows , so it 's got to have 2 columns , but i could m... | should not all the `` o '' 's of same order ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | so , we know that 0 times anything is equal to 0 . or , anything times 0 is equal to 0 . so what would be the analogy if we 're thinking about matrix multiplication ? | why does sal draw a arrow after some of his equal signs ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | you multiply 1 times any number , you get that number again . and that essentially inspired our thinking behind having identity matrices . said hey , maybe there are some matrices that if i multiply times some other matrix , i 'm going to get that matrix again . | what 's the practical use of zero matrices ? |
: we 've been drawing analogies between i guess we could say traditional multiplication , or scalar multiplication , and the first one we drew is when you have traditional multiplication , you multiply 1 times any number and you get that number again . and you could view 1 as essentially the identity . the identity nu... | the identity number , or this is the identity property of multiplication . you multiply 1 times any number , you get that number again . and that essentially inspired our thinking behind having identity matrices . said hey , maybe there are some matrices that if i multiply times some other matrix , i 'm going to get th... | the number of non zero diagonal matrices of order 3 , ifa^2=a is ? |
functionalism is a system of thinking based on the ideas of emile durkheim that looks at society from a large scale perspective . it examines the necessary structures that make up a society and how each part helps to keep the society stable . according to functionalism , society is heading toward an equilibrium . i kno... | it is always there , but we do n't notice it until we try and break it or act against it . some other examples are moral regulations , religious faiths , and social currents like suicide or birth rate . you might wonder how suicide can be a social fact . | also , if morality ( being moral ) is a social fact , why are people immoral and why do they do things that are considered unmoral like murders and robbery ? |
functionalism is a system of thinking based on the ideas of emile durkheim that looks at society from a large scale perspective . it examines the necessary structures that make up a society and how each part helps to keep the society stable . according to functionalism , society is heading toward an equilibrium . i kno... | functionalism is a system of thinking based on the ideas of emile durkheim that looks at society from a large scale perspective . it examines the necessary structures that make up a society and how each part helps to keep the society stable . | how does functionalism classify the large nations that existed before schools , hospitals , and written constitutions were widespread ? |
functionalism is a system of thinking based on the ideas of emile durkheim that looks at society from a large scale perspective . it examines the necessary structures that make up a society and how each part helps to keep the society stable . according to functionalism , society is heading toward an equilibrium . i kno... | and everyone becomes dependent on one another for their continued well being . people have become specialized , which forces mutual interdependence . this interdependence helps to ensure that the community wo n't fall apart . | why does change threaten the interdependence of people ? |
functionalism is a system of thinking based on the ideas of emile durkheim that looks at society from a large scale perspective . it examines the necessary structures that make up a society and how each part helps to keep the society stable . according to functionalism , society is heading toward an equilibrium . i kno... | they have a coercive effect over the individual that is usually only noticed when we resist against them . so for example , one social fact is the law . it is always there , but we do n't notice it until we try and break it or act against it . | ok so is `` law '' an institution or a social fact ? |
functionalism is a system of thinking based on the ideas of emile durkheim that looks at society from a large scale perspective . it examines the necessary structures that make up a society and how each part helps to keep the society stable . according to functionalism , society is heading toward an equilibrium . i kno... | functionalism is a system of thinking based on the ideas of emile durkheim that looks at society from a large scale perspective . it examines the necessary structures that make up a society and how each part helps to keep the society stable . | is durkheim really the one responsible for functionalism ? |
functionalism is a system of thinking based on the ideas of emile durkheim that looks at society from a large scale perspective . it examines the necessary structures that make up a society and how each part helps to keep the society stable . according to functionalism , society is heading toward an equilibrium . i kno... | and everyone becomes dependent on one another for their continued well being . people have become specialized , which forces mutual interdependence . this interdependence helps to ensure that the community wo n't fall apart . | can someone give me an easy definition of interdependence , please ? |
functionalism is a system of thinking based on the ideas of emile durkheim that looks at society from a large scale perspective . it examines the necessary structures that make up a society and how each part helps to keep the society stable . according to functionalism , society is heading toward an equilibrium . i kno... | the individual is acknowledged , but nothing they do really affects the structures of society . functionalism is also largely unable to explain social change and conflict . we know it happens , but functionalism is so focused on maintaining the equilibrium of the society that little significant change is modeled and no... | what are the factors that affect roles of traditional rulers in conflict management ? |
functionalism is a system of thinking based on the ideas of emile durkheim that looks at society from a large scale perspective . it examines the necessary structures that make up a society and how each part helps to keep the society stable . according to functionalism , society is heading toward an equilibrium . i kno... | and laws maintain social order . these recognized and intended consequences of institutions are known as manifest functions . but sometimes the institutions have unintended consequences . schools allow the students and professors to make social connections , and they expose the students to new activities through extrac... | what are the roles of institutions in the development process ? |
functionalism is a system of thinking based on the ideas of emile durkheim that looks at society from a large scale perspective . it examines the necessary structures that make up a society and how each part helps to keep the society stable . according to functionalism , society is heading toward an equilibrium . i kno... | one structure is institutions , which are structures that meet the needs of the society , like education systems , financial institutions , businesses and marriage , laws , mass media , nongovernmental organizations , medicine , religion , the military , police forces , and lots of others , too . another structure is w... | someone help me , please : what is the difference between social facts and conservative ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | that 'll become important later on . the signal that this neuron is sending is no , or nitric oxide . this neuron is actually from a division of the nervous system called the parasympathetic nervous system , or the psns . | so , just to clarify the concept , would something like viagra contain nitric oxide to cause erection ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | so you can see visually that the arterials on this side are much more dilated , that is , they let in a lot more blood , thus can cause an erection . what 's keeping this penis flaccid ? what is keeping these arterials from opening up ? | why does the sympathetic system keep the penis flaccid then ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | remember , now that we 're erect , we 've filled these vascular chambers here with blood . the first part is sympathetic nervous system stimulated . remember , in red we drew these neurons , the sympathetic nervous system neurons . | could you please clarify whether it is nitrus oxide from the parasympathetic nervous system or norepinephrine from the sympathetic nervous system that is released to cause an erection ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | when you 're physically or mentally sexually stimulated by sights or sounds , or smells , or even thoughts , your brain sends signals to your penis , and it can cause an erection . it does that by sending signals to the blood vessels in the penis , and those signals cause those blood vessels to open up , and allow bloo... | where does the blood come from when a female gets her period ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | remember , now that we 're erect , we 've filled these vascular chambers here with blood . the first part is sympathetic nervous system stimulated . remember , in red we drew these neurons , the sympathetic nervous system neurons . | around vishal says that the sympathetic nervous system is responsible for stimulating the various reproductive structures by releasing norepinephrine , but did n't we learn that norepinephrine is responsible for keeping the penis flaccid , whereas no from the parasympathetic nervous system is responsible for the arous... |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | we 'll start with a definition . what is ejaculation ? ejaculation is the discharge of semen from the penis . | after the ejaculation , how does sperms reach the ovum ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | this one on the left here is flaccid . this one over here on the right is erect . the reason why the one on the left is flaccid , is because it has arterials that are constricted . | the ovum is supposed to be present in the ovi-duct right ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . | how will sperms reach till there ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | what is ejaculation ? ejaculation is the discharge of semen from the penis . you normally discharge about three to five milliliters per ejaculation . | does urine and semen come out of the same `` hole '' in the penis or different ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | as these arterials dilate and allow lots of blood into these sinuses here , they actually fill so much that they push outward against the edges and compress the veinous drainage of the penis . that basically prohibits flaccidity , thus , it results in an erection . just to be complete , an erection is reversed when the... | is n't an orgasm and an erection basically the same thing ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | we 'll start with a definition . what is ejaculation ? ejaculation is the discharge of semen from the penis . | in ejaculation , is 3-5ml of blood expelled with the sperm inside ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | i 'm still confused in how sperms enter the female reproductive system ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | the signal that this neuron is sending is no , or nitric oxide . this neuron is actually from a division of the nervous system called the parasympathetic nervous system , or the psns . as these arterials dilate and allow lots of blood into these sinuses here , they actually fill so much that they push outward against t... | and 0 can nitrous oxide from the environment stimulate this in the same way the nervous system does ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | for example , you see a decrease in heart rate and blood pressure after ejaculation . in some , the process of ejaculation and the whole body physiological changes , is called an orgasm . | what are the advantages of orgasm for man ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | how sperm knows its direction to fertilize the egg ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | why do people need to have reproductive systems to live ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | in that three to five milliliters , you actually pack about 300 million sperm . an ejaculation happens when , basically , a critical level of sexual excitement has been reached . sexual stimulation actually causes nerves in the penis to send chemical signals to the spinal cord and brain . | can erection happen without the need for sexual sight , smell , or excitement ? |
we 're gon na talk about the transport of sperm . i just mean how it gets transported out of the male reproductive tract , and into the female reproductive tract , where it can hopefully fertilize an egg , and result in a pregnancy . to do this , we 're gon na first look at a sagittal view of the male reproductive sys... | what is ejaculation ? ejaculation is the discharge of semen from the penis . you normally discharge about three to five milliliters per ejaculation . | if the semen acts as a buffer in the urine that 's coming out of the penis , than when a male is having intercourse , does that mean that he is urinating into the women 's vagina ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . | does l'hopital 's rule apply here ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so defined this way , f of x is equal to x plus 3 . so if this is 1 , 2 , 3 , we have a y-intercept at 3 and then the slope is 1 . and it 's defined for all x 's except for x is equal to 2 . | how did sal come up with a slope of 1 ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . | one question , if you use algebraic rules on it , like sal did and you cancel the ( x-2 ) out , after that the function f ( x ) is not the same as before or ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . | say i have lim of 5/x-7 as x - > 7 i know it is undefined but say i have lim 5/ ( x-7 ) ^2 as x - > 7 why is it +infinity rather than undefined ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . | i did n't get it ... when we have f ( x ) = ( x^2 + x -6 ) /x-2..then our limf ( x ) as x approaches 2 is not defined..but when w simplified the unction to x+3 then we got a different value of limit as x approaches 2 ..can we have two values for same limit..of the same function ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . | if lim f ( x ) = lim g ( x ) x - > 1 x - > 1 can you say that lim f ( x ) /g ( x ) = 1 when x - > 1 is always true ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . | or it would be correct only as long as lim g ( x ) does not equal to 0 when x - > 1 ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . | if you solved ( x+3 ) ( x-2 ) you get x^2-6 , which does n't = x^2+x-6 , am i missing something ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so defined this way , f of x is equal to x plus 3 . so if this is 1 , 2 , 3 , we have a y-intercept at 3 and then the slope is 1 . and it 's defined for all x 's except for x is equal to 2 . | or , in the case of derivatives , the slope of a segment that is infinetesimally small is the slope of the curve at a single discrete moment ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so it seems to be approaching this value right over there . similarly , as we approach 2 from values greater than it , if we 're at , i do n't know , this could be like 2.5 , 2.5 our f of x is right over there . if we get even closer to 2 , our f of x is right over there . | for the equation could n't i plug in 1.9999 and 2.0001 directly into the original equation ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so if we want to rewrite this , we can rewrite the top expression . and this just goes back to your algebra one , two numbers whose product is negative 6 , whose sum is positive 3 , well that could be positive 3 and negative 2 . so this could be x plus 3 times x minus 2 , all of that over x minus 2 . | while finding the limit if a root , why do usually take the positive value and not the negative value ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so defined this way , f of x is equal to x plus 3 . so if this is 1 , 2 , 3 , we have a y-intercept at 3 and then the slope is 1 . and it 's defined for all x 's except for x is equal to 2 . | .. how did sal find the slope as 1 ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . | what is i'hopital '' s rule ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so defined this way , f of x is equal to x plus 3 . so if this is 1 , 2 , 3 , we have a y-intercept at 3 and then the slope is 1 . and it 's defined for all x 's except for x is equal to 2 . | how many nines after a decimal equals to an integer 1 ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so looking at it this way , if we just evaluate f of 2 , on our numerator , we get 2 squared plus 2 minus 6 . so it 's going to be 4 plus 2 , which is 6 , minus 6 , so you 're going to get 0 in the numerator and you 're going to get 0 in the denominator . so we do n't have , the function is not defined , so not defined... | 0/0 is known to be undefined , so why factor it through ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so let 's call this the y-axis call it y equals f of x . and then let 's , over here , let me make a horizontal line , that is my x-axis . so defined this way , f of x is equal to x plus 3 . | how do u know where to draw the line ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . | why did people determine that x/0 is undefined ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so there 's no simple thing there . even if this did evaluate , if it was a continuous function , then the limit would be whatever the function is , but that does n't necessarily mean the case . but we see very clearly the function is not defined here . so let 's see if we can simplify this and also try to graph it in ... | does somebody know a function , where you get a wrong result , if you simplify that function and then enter an undefined value , whose limit you are looking for ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so there 's no simple thing there . even if this did evaluate , if it was a continuous function , then the limit would be whatever the function is , but that does n't necessarily mean the case . but we see very clearly the function is not defined here . | how would i define the limit of a function with more than one possible value ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . | why are we trying to simplify or obtain a different form of the expression f ( x ) ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . | since we got 0/0 on direct substitution of x=2 in f ( x ) , ca n't we just say the limit is indeterminate ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so defined this way , f of x is equal to x plus 3 . so if this is 1 , 2 , 3 , we have a y-intercept at 3 and then the slope is 1 . and it 's defined for all x 's except for x is equal to 2 . | how do we know the slope is 1 ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so defined this way , f of x is equal to x plus 3 . so if this is 1 , 2 , 3 , we have a y-intercept at 3 and then the slope is 1 . and it 's defined for all x 's except for x is equal to 2 . | at 3.00 min , how slope is found , and why hole at 3 ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | now given this , let 's try to answer our question . what is the limit of f of x as x approaches 2 . well , we can look at this graphically . | what is the limit of 1/ ( x-1 ) as x approaches 1 ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . | lim x -- > 0 ( 3x+|x| ) / ( 7x-5|x| ) lim x -- > 0+ ( 3x+x ) / ( 7x-5x ) as x > 0 lim x -- - > 0+ 4x/2x lim x -- - > 0+ 2 =2 right hand limit of the function is 2 lim x -- - > 0- ( 3x- ( -x ) ) / ( 7x- ( -5x ) = 2 so limit exists right ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . | what will be the limit of x*sin ( 1/x ) when x tends to 0 and how ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . | will it be 1 as sin ( x ) /x = 1 ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . | is n't it true that if we transform a function f ( x ) = ( x^2+x-6 ) /x-2 according to all rules and we do it properly then simplyfied function f ( x ) =x+3 should be equal to it ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so there 's no simple thing there . even if this did evaluate , if it was a continuous function , then the limit would be whatever the function is , but that does n't necessarily mean the case . but we see very clearly the function is not defined here . so let 's see if we can simplify this and also try to graph it in ... | how come transformed function is n't just the same function ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so we could say this is equal to x plus 3 for all x 's except for x is equal to 2 . so that 's another way of looking at it . another way we could rewrite our f of x , we 'll do it in blue , just to change the colors , we could rewrite f of x , this is the exact same function , f of x is equal to x plus 3 when x does n... | calculus works in a different way than the rules of algebra indicate ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | and this just goes back to your algebra one , two numbers whose product is negative 6 , whose sum is positive 3 , well that could be positive 3 and negative 2 . so this could be x plus 3 times x minus 2 , all of that over x minus 2 . so as long as x does not equal 2 , these two things will cancel out . | if the original is ( x+3 ) ( x-2 ) /x-2 , should't x also ca n't equal to 3 either ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | now this wo n't always be the limit , even if it 's defined , but it 's a good place to start , just to see if it 's something reasonable could pop out . so looking at it this way , if we just evaluate f of 2 , on our numerator , we get 2 squared plus 2 minus 6 . so it 's going to be 4 plus 2 , which is 6 , minus 6 , s... | ok uuuhm is it safe to just substitute '2 ' to the simplified expression ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | and this just goes back to your algebra one , two numbers whose product is negative 6 , whose sum is positive 3 , well that could be positive 3 and negative 2 . so this could be x plus 3 times x minus 2 , all of that over x minus 2 . so as long as x does not equal 2 , these two things will cancel out . | could you just plug in 2 into x+3 since you were able to cross out the ( x-2 ) in the numerator and the denominator and get 5 ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | but we see very clearly the function is not defined here . so let 's see if we can simplify this and also try to graph it in some way . so one thing that might have jumped out at your head is you might want to factor this expression on top . | why is n't the graph a parabola ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . | why does sal make a slant line while graphing f ( x ) ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so there 's no simple thing there . even if this did evaluate , if it was a continuous function , then the limit would be whatever the function is , but that does n't necessarily mean the case . but we see very clearly the function is not defined here . | what does sal mean with the continuous function mention 0 ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . | was wondering what is meant by the 'sandwich theorem '' ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so looking at it this way , if we just evaluate f of 2 , on our numerator , we get 2 squared plus 2 minus 6 . so it 's going to be 4 plus 2 , which is 6 , minus 6 , so you 're going to get 0 in the numerator and you 're going to get 0 in the denominator . so we do n't have , the function is not defined , so not defined... | so why ca n't you find the limit of the numerator :0 and then the limit of the denominator : 0 and say that the limit does not exist ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so this is x is equal to 1 , x is equal to 2 . so when x is equal to 2 it is undefined . so let me make sure i can , so it 's undefined right over there . | so , when unsimplified equations are used as functions , are they essentially the same as their simplified versions , with the only differences being any discontinuities/undefined solutions added because of the seemingly-superfluous content so to speak ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | so this is x is equal to 1 , x is equal to 2 . so when x is equal to 2 it is undefined . so let me make sure i can , so it 's undefined right over there . | or i guess in other words , unsimplified equations are used as functions to describe a trend but also include some undefined solution ( s ) ? |
let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . now the first attempt that you might want to do right when you see something like this , is just see what happens what is f of 2 . now this wo n't always be ... | let 's say that f of x is equal to x squared plus x minus 6 over x minus 2 . and we 're curious about what the limit of f of x , as x approaches 2 , is equal to . | why does `` x^2 + x - 6 '' become `` ( x + 3 ) ( x - 2 ) '' ? |
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