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use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , what does e mean ? e is just a number , just like pi is just a number . | what is an mathematical explation of what e stands for ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | actually that makes sense because it 's actually closer to 3 . 2.71 is closer to 3 than it is to 2 . so this feels right , that you take this to the fourth , little over the fourth power , you get to 67 . | i was wondering , when considering the expression ln ( 2e ) ^2 , does the the square belong to the `` ln '' function as a whole or does it belong to the `` 2e '' separately ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | if you have a graphing calculator like this , you literally can literally type in the statement natural log of 67 then evaluate it . so here this is the button for ln , means natural log , log natural , maybe . ln of 67 , and then you press enter , and it 'll give you the answer . | i 'm confused about how to solve natural logarithms when there is something like : 5 ln ( 6x ) = 8 can someone help me to figure it out ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | if you have a graphing calculator like this , you literally can literally type in the statement natural log of 67 then evaluate it . so here this is the button for ln , means natural log , log natural , maybe . ln of 67 , and then you press enter , and it 'll give you the answer . | how would i go about finding the number whose natural log is a given number ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , what does e mean ? e is just a number , just like pi is just a number .... | like pi=22/7 can e be represented in fractions ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . | how do you find natural logs without a calculator ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | so you could view log base e as 67 . let 's see , what does e mean ? e is just a number , just like pi is just a number . so this is really the same thing as saying log base 2.71 , and the actual numbers , so you 'd have to write all the digits that keep on going forever and never repeat 6 of 67 . | due to euler 's identity does that not mean that the ln of any algebraic number is transcendental as e^x , if x is algebraic , equals a transcendental number ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , what does e mean ? | how is log different than e ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | actually that makes sense because it 's actually closer to 3 . 2.71 is closer to 3 than it is to 2 . so this feels right , that you take this to the fourth , little over the fourth power , you get to 67 . | how would you find ln 3x=2 ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | actually that makes sense because it 's actually closer to 3 . 2.71 is closer to 3 than it is to 2 . so this feels right , that you take this to the fourth , little over the fourth power , you get to 67 . | how do we simplify expressions such as 2^2x4^3x/16x ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | if you have a graphing calculator like this , you literally can literally type in the statement natural log of 67 then evaluate it . so here this is the button for ln , means natural log , log natural , maybe . ln of 67 , and then you press enter , and it 'll give you the answer . | what does log 3 x mean ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | and if you think about what 2 to the fourth power gets you to 16 . and 3 to the fourth power gets you to 81 . 67 is between 16 and 81 and e is between 2 and 3 . | is it like base 3 with power x or you just multiply 3 with x ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | so this is the same thing as log base e of 67 . this is saying the exact same thing . to what power do i have to raise e to to get 67 ? | what is the exact calculator sal is using ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | you 're saying e to the x is equal to 67 , we need to figure out what x is . now , traditionally you will never see someone write log base e even though e is one of the most common bases to take a logarithm of . and so the reason why you would n't see log base e written this way is log base e is referred to as the natu... | i know e is common but why take a logarithm with e as a base ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | now , traditionally you will never see someone write log base e even though e is one of the most common bases to take a logarithm of . and so the reason why you would n't see log base e written this way is log base e is referred to as the natural logarithm . and i think that 's used because e shows up so many times in ... | is there a relationship between the natural logarithm ( for argument 's sake i 'll say ln ( n ) ) and the rule that ( 1+ ( 1/n ) ) ^n approximately equals e ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | the digit after that is 5 or larger , it 's a 6 , so we 're going to round up . so this is 4.205 . so this is approximately equal to 4.205 . | how do you solve for n when -4e^ ( n+4 ) = -83 ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , what does e mean ? e is just a number , just like pi is just a number .... | is it impossible because of the infinite number of digits in e ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . | what is the integration of cot2xdx/ ( -9sin2x-csc2x ) ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | if you have a graphing calculator like this , you literally can literally type in the statement natural log of 67 then evaluate it . so here this is the button for ln , means natural log , log natural , maybe . ln of 67 , and then you press enter , and it 'll give you the answer . | can someone help me figure out how to solve ln ( 2x-1 ) -1=0 ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | now , traditionally you will never see someone write log base e even though e is one of the most common bases to take a logarithm of . and so the reason why you would n't see log base e written this way is log base e is referred to as the natural logarithm . and i think that 's used because e shows up so many times in ... | how would you solve log base 5 ( 13 ) by using common logs or natural logs and a calculator ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | actually that makes sense because it 's actually closer to 3 . 2.71 is closer to 3 than it is to 2 . so this feels right , that you take this to the fourth , little over the fourth power , you get to 67 . | how would you expand the expression : ln20x^3 y^2 ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | so what power do i have to raise e to to get to 67 ? so another way of saying that is this is equal to x . you 're saying e to the x is equal to 67 , we need to figure out what x is . now , traditionally you will never see someone write log base e even though e is one of the most common bases to take a logarithm of . | how can i apply logarithms to x-3^x=6 ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | if you have a graphing calculator like this , you literally can literally type in the statement natural log of 67 then evaluate it . so here this is the button for ln , means natural log , log natural , maybe . ln of 67 , and then you press enter , and it 'll give you the answer . | when do you use natural log and when do you use regular logarithms ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , what does e mean ? | i mean , what 's the point of using a log with base e when you could just use something simple like log with base 10 ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | if you have a graphing calculator like this , you literally can literally type in the statement natural log of 67 then evaluate it . so here this is the button for ln , means natural log , log natural , maybe . ln of 67 , and then you press enter , and it 'll give you the answer . | why is the natural log of a non-positive number not defined ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | and if you think about what 2 to the fourth power gets you to 16 . and 3 to the fourth power gets you to 81 . 67 is between 16 and 81 and e is between 2 and 3 . | how do you find 3.03=1.086 to the power x without using log ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | if you have a graphing calculator like this , you literally can literally type in the statement natural log of 67 then evaluate it . so here this is the button for ln , means natural log , log natural , maybe . ln of 67 , and then you press enter , and it 'll give you the answer . | how do you do natural logs without calculators ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | if you have a graphing calculator like this , you literally can literally type in the statement natural log of 67 then evaluate it . so here this is the button for ln , means natural log , log natural , maybe . ln of 67 , and then you press enter , and it 'll give you the answer . | how do you simplify ln ( 2e ) ^2 + ln ( ( 4e^6 ) ^0.5 ) - ln ( 8e^7 ) without the use of a calculator ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | the digit after that is 5 or larger , it 's a 6 , so we 're going to round up . so this is 4.205 . so this is approximately equal to 4.205 . | how long will i t take for $ 4,000 to grow to $ 17,000 if the money is invested at 7.7 % compounded quarterly ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . | why use 'e ' when you get an approximation ? |
use a calculator to find log base e of 67 to the nearest thousandth . so just as a reminder , e is one of these crazy numbers that shows up in nature , in finance , and all these things , and it 's approximately equal to 2.71 and it just keeps going on and on and on . so you could view log base e as 67 . let 's see , w... | so this is approximately equal to 4.205 . and it actually makes a lot of sense , because we know that e is greater than 2 , and it is less than 3 . and if you think about what 2 to the fourth power gets you to 16 . | so does anyone know , how to calculate using the book ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | so divide both sides by 2 , so the force that i pulled down with is 5 newtons . so i pulled down 5 newtons for 2 meters , and it pulls up a 10-newton weight for 1 meter . force times distance is equal to force times distance . | why would the 2 ropes on the left side move only 1 meter ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | and let 's say i have a rope going over that pulley . that 's my rope . and at this end , let 's say i have a weight , a 10-newton weight , and i 'm going to pull down on this end to make the weight to go up . | how does the rope move if it 's attached to the ceiling ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | and let 's say i have a rope going over that pulley . that 's my rope . and at this end , let 's say i have a weight , a 10-newton weight , and i 'm going to pull down on this end to make the weight to go up . | since you 're pulling on the rope , should n't the rope be enlengthened overall , and so the rope is only moving 1ft upwards in the middle ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | because it gives you mechanical advantage . so if i have this wedge here . and this is a 30-degree angle , if this distance up here , let 's call this distance d , what is this distance going to be ? | is there a difference between an inclined plane and a wedge ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | it 's 5d joules . this is n't some kind of units . it 's 10 newtons times the distance that we 're up , and that 's 1/2d , so it 's 5d joules . | is n't the ground just an arbitrarily defined surface ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | if i take a box , and i push it with some force all the way up here , what is the mechanical advantage of this system ? well , when the box is up here , we know what its potential energy is . its potential energy is going to be the weight of the box . so let 's say this is a 10-newton box . | can you increase the potential energy by digging a hole in the ground beneath it ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | if i take a box , and i push it with some force all the way up here , what is the mechanical advantage of this system ? well , when the box is up here , we know what its potential energy is . its potential energy is going to be the weight of the box . so let 's say this is a 10-newton box . | if you were to define the surface of the table as the ground , would the box have no potential energy ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | that 's my rope . and at this end , let 's say i have a weight , a 10-newton weight , and i 'm going to pull down on this end to make the weight to go up . so my question to you is what is the mechanical advantage of this system ? | would the weight of the pulley holding the weight be significant ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | so i pulled down 5 newtons for 2 meters , and it pulls up a 10-newton weight for 1 meter . force times distance is equal to force times distance . so what was the input force ? the input force is equal to 5 newtons and the output force of this machine is equal to 10 newtons . mechanical advantage is the output over the... | so if the mechanical advantage of a machine is greater than 1 i.e the input force applied is less than the output force , does that mean that the machine is more efficient ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | and why is a wedge a machine ? because it gives you mechanical advantage . so if i have this wedge here . | everything that gives a mechanical advantage is a machine right ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | so when i pull the rope down 2 feet here , this weight only moves up 1 foot . so what is the work that i 'm doing ? well , the work in is the same as the work out , and we know what the work out is . the work out is going to be the force that this contraption or this machine is pulling upwards with , and that 's 10 new... | does a pulley system reduce the amount of work that you have to do ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | so my rope starts up going up like that , then it comes back down , comes around the second pulley , and now this is attached to the ceiling up here . the second pulley is actually where the weight is attached to . and let 's just call it a 10-newton weight again , although it does n't really matter what the weight is ... | is the 10 newton weight tied onto the string on the pulley ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | it 's 5d joules . this is n't some kind of units . it 's 10 newtons times the distance that we 're up , and that 's 1/2d , so it 's 5d joules . | should n't gravity be included ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | well , it 's the force output , 10 newtons , divided by the force input , 5 newtons . the mechanical advantage is 2 . | how would the system of pulleys be and would there still be mechanical advantage ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | so i pulled down 5 newtons for 2 meters , and it pulls up a 10-newton weight for 1 meter . force times distance is equal to force times distance . so what was the input force ? | concerning the ending when he says fi= 5n , how would that force displace the object ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | so i pulled down 5 newtons for 2 meters , and it pulls up a 10-newton weight for 1 meter . force times distance is equal to force times distance . so what was the input force ? | would n't the parallel force from gravity be equal to 5n , therefore canceling the pushing force and resulting in acceleration=0 ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | and let 's say i have a rope going over that pulley . that 's my rope . and at this end , let 's say i have a weight , a 10-newton weight , and i 'm going to pull down on this end to make the weight to go up . | is the rope in the system immovable as it is fixed ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | so i pulled down 5 newtons for 2 meters , and it pulls up a 10-newton weight for 1 meter . force times distance is equal to force times distance . so what was the input force ? | i do n't understand how a 5n force would move the box , should n't it just balance the force of gravity ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | so my question to you is what is the mechanical advantage of this system ? what is the force that i have to pull down in order to lift this weight , this 10-newton weight in order to produce 10 newtons of force upwards ? well , in any pulley situation -- and i do n't know if textbooks cover it this way , but this is ho... | how would a force lighter than a feather weigh down a heavy weight on a old fashion pulley ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | because it gives you mechanical advantage . so if i have this wedge here . and this is a 30-degree angle , if this distance up here , let 's call this distance d , what is this distance going to be ? | does a wedge have to be right triangle , or can it be any triangle ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | so let 's say over here at the top , i still have the same pulley that 's attached to the ceiling , but i 'm going to add slight variation here . i have another pulley here . and now let me do the other pulley down here . | am i wrong in assuming that the the pulley drawn is free to move up and down ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | well , it 's the force output , 10 newtons , divided by the force input , 5 newtons . the mechanical advantage is 2 . | also , does the vertical mobility of that pulley determine if there would be mechanical advantage ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | so divide both sides by 2 , so the force that i pulled down with is 5 newtons . so i pulled down 5 newtons for 2 meters , and it pulls up a 10-newton weight for 1 meter . force times distance is equal to force times distance . | why would the 2 ropes on the left side move only 1 meter ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | so let 's say this is a 10-newton box . the potential energy at this point is going to be 10 newtons times its height . so potential energy at this point has to equal 10 newtons times the height , which is going to be 5 joules . and that 's also the amount of work one has to put into the system in order to get it into ... | should n't the potential energy be 5d j , not just 5 j , since the height is 1/2d ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | and if this is getting 1 foot shorter , and this is one getting 1 foot shorter , it makes sense this whole thing is getting 2 feet shorter . but the important thing to realize , if each of these are getting 1 foot shorter , then this weight is only moving up 1 foot . so when i pull the rope down 2 feet here , this weig... | by saying the pe is only 5j , is the assumption being made that d = 1 ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | well , i know the distance that i pulled down . i know i pulled down 2 meters . so i pulled down 2 meters , so this has to equal the force times the distance . | how did you know to label the opposite side d/2 and the hypotenuse , d ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | well , it 's going to be d sine of 30 . and we know that the sine of 30 degrees , hopefully by this point , is 1/2 , so this is going to be 1/2d . you might want to review the trigonometry a little bit if that does n't completely ring a bell for you . | what if the angle was 60 degrees ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | well , in any pulley situation -- and i do n't know if textbooks cover it this way , but this is how i think about it , because you do n't have to memorize formulas . i just think about , well , what happens to the lengths of rope ? or what is the total distance that the object you 're trying to move travels ? | how would the lengths change ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | so i pulled down 5 newtons for 2 meters , and it pulls up a 10-newton weight for 1 meter . force times distance is equal to force times distance . so what was the input force ? | when considering the force it takes to push the box up the wedge , do n't you have to consider the force of gravity as it relates to the angle you 're pushing up at ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | well , it 's the force output , 10 newtons , divided by the force input , 5 newtons . the mechanical advantage is 2 . | if i just pushed the box at a very flat slope over a distance of 500m would i have a mechanical advantage of 1000 ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | it 's 5d joules . this is n't some kind of units . it 's 10 newtons times the distance that we 're up , and that 's 1/2d , so it 's 5d joules . | why does n't sal include g ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . | why are levers pulleys and wedges called `` simple '' machines ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | let 's see if we can do another mechanical advantage problem . actually , let 's do a really simple one that we 've really been working with a long time . let 's say that i have a wedge . | what are actually `` simple '' machines ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me start with a very simple pulley . | how do they differ from compound machines and again , what are `` compound '' machines ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | well , it 's the force output , 10 newtons , divided by the force input , 5 newtons . the mechanical advantage is 2 . | is it possible to have a block and tackle system with a mechanical advantage of 3 and a velocity ratio of 2 ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | welcome back . now let 's do some more mechanical advantage problems . | is a efficiency over 100 possible ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | and if this is getting 1 foot shorter , and this is one getting 1 foot shorter , it makes sense this whole thing is getting 2 feet shorter . but the important thing to realize , if each of these are getting 1 foot shorter , then this weight is only moving up 1 foot . so when i pull the rope down 2 feet here , this weig... | would the weight move only 1 foot for every 3 i pulled or would it still be equal to half of what i pulled , so 1.5 ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | if i take a box , and i push it with some force all the way up here , what is the mechanical advantage of this system ? well , when the box is up here , we know what its potential energy is . its potential energy is going to be the weight of the box . so let 's say this is a 10-newton box . | in the wedge example , why was gravity not included when figuring out the potential energy ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | well , it 's the force output , 10 newtons , divided by the force input , 5 newtons . the mechanical advantage is 2 . | what is the relationship between the angle of incline of a frictionless wedge , and its mechanical advantage ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | and that makes sense , because i have to pull twice as much for this thing to move up half of that distance . let 's see if we can do another mechanical advantage problem . actually , let 's do a really simple one that we 've really been working with a long time . | i can see the 30-60-90 trig and how that works out , so is there some sort of optimal angle for which you have a maximum mechanical advantage ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | welcome back . now let 's do some more mechanical advantage problems . | what is the velocity ratio ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | but if this length of rope is getting 2 feet shorter , what is this length of rope getting ? well , this entire length of rope is also going to get 2 feet shorter , this entire length of rope right here . but this entire length of rope is split between this side -- let me do it in different color -- between this side a... | so we must also include the mass of the rope ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | and let 's say i have a rope going over that pulley . that 's my rope . and at this end , let 's say i have a weight , a 10-newton weight , and i 'm going to pull down on this end to make the weight to go up . | i am just not able to understand that on pulling the rope how can the weight equally divide the 2feet pulled between the two ropes towards the left.please help me clear this doubt ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | i should n't mix english and metric system . so 10 newtons times 1 meter , so it equals 10 joules . and this has to be the work that i 've put into it , too , right ? | i have a dout about the block since it 's potential energy is 10n means mass is 1 m and h=1 p.e=1.10.1=10n is it right ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | but let 's say i have that little disk where the rope goes over and it rolls so that the rope can go over it and move without having a lot of friction . and let 's say i have a rope going over that pulley . that 's my rope . and at this end , let 's say i have a weight , a 10-newton weight , and i 'm going to pull down... | is n't the box connected to the second pulley so it should just hang there and just the rope should move ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | so this input force -- oh , sorry , this is going to be -- sorry , this is n't 5 joules . it 's 10 times 1/2 times the distance . it 's 5d joules . | 4 , why is n't pe 10 x 1/2 x g ( 9.81 ) ? |
welcome back . now let 's do some more mechanical advantage problems . and in this video , we 'll focus on pulleys , which is another form of a simple machine . and we 've done some pulley problems in the past , but now we 'll actually understand what the mechanical advantage inherent in these machines are . so let me ... | welcome back . now let 's do some more mechanical advantage problems . | is there a difference between pe and gravitational pe ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | if you give me an x value that 's between a and b , it 'll tell you the area under lowercase f of t between a and x . now the cool part , the fundamental theorem of calculus . the fundamental theorem of calculus tells us -- let me write this down because this is a big deal . | when defining fundamental theorem of calculus should n't the function of lower limit of the integral be zero ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | so all fair and good . uppercase f of x is a function . if you give me an x value that 's between a and b , it 'll tell you the area under lowercase f of t between a and x . | sal says that every continous function has an anti-derivative.but there are continous functons like sin ( x ) /x which is undefined only at x=0 .but still it is not possible to find the anti-derivative of this function over any interval which excludes 0 ... .why is that ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | well , how do we denote the area under the curve between two endpoints ? well , we just use our definite integral . that 's our riemann integral . it 's really that right now before we come up with the conclusion of this video , it really just represents the area under the curve between two endpoints . | why lower limit 'a ' of integral does n't show the result differentiating the integral ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | this right over here was our a . and notice , it does n't matter what the lower boundary of a actually is . you do n't have anything on the right hand side that is in some way dependent on a . anyway , hope you enjoyed that . | in other words , why 'a ' does n't influence the calculations ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | i 'm going to label my horizontal axis t so we can save x for later . i can still make this y right over there . and let me graph . | so i 'm wandering how time still flows from a second to the next ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | well , it tells us that for any continuous function f , if i define a function , that is , the area under the curve between a and x right over here , that the derivative of that function is going to be f. so let me make it clear . every continuous function , every continuous f , has an antiderivative capital f of x . t... | what is the difference between capital f ( x ) and small f ( x ) in this video ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | if you give me an x value that 's between a and b , it 'll tell you the area under lowercase f of t between a and x . now the cool part , the fundamental theorem of calculus . the fundamental theorem of calculus tells us -- let me write this down because this is a big deal . | is there any proof for the fundamental theorem of calculus ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | well , how do we denote the area under the curve between two endpoints ? well , we just use our definite integral . that 's our riemann integral . | what 's the difference between indefinite and definite integrals ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | now we see it has a connection to derivatives . well , how would you actually use the fundamental theorem of calculus ? well , maybe in the context of a calculus class . | when given the graph of the derivative and a point on the function , how can you use the fundemental theorem of calculus to find another point on the function ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | this right over here was our a . and notice , it does n't matter what the lower boundary of a actually is . you do n't have anything on the right hand side that is in some way dependent on a . | why does n't it matter which 'a ' to take ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | let me do this in a new color just to show this is an example . let 's say someone wanted to find the derivative with respect to x of the integral from -- i do n't know . i 'll pick some random number here . | is n't derivative the slope of the tangent line at a point in a curve ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | it connects differential calculus and integral calculus -- connection between derivatives , or maybe i should say antiderivatives , derivatives and integration . which before this video , we just viewed integration as area under curve . now we see it has a connection to derivatives . | and is n't integral an area under a curve ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | so let 's define some new function to capture the area under the curve between a and x . well , how do we denote the area under the curve between two endpoints ? well , we just use our definite integral . that 's our riemann integral . it 's really that right now before we come up with the conclusion of this video , it... | so how can we have a derivative of an integral - a `` slope of tangent line '' of an `` area '' ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | if you give me an x value that 's between a and b , it 'll tell you the area under lowercase f of t between a and x . now the cool part , the fundamental theorem of calculus . the fundamental theorem of calculus tells us -- let me write this down because this is a big deal . | why does n't the value of the variable `` a '' matter in the fundamental theorem ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | it connects differential calculus and integral calculus -- connection between derivatives , or maybe i should say antiderivatives , derivatives and integration . which before this video , we just viewed integration as area under curve . now we see it has a connection to derivatives . | how do we know that the area can be represented by the antiderivative ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | why does it get such an important title as the fundamental theorem of calculus ? well , it tells us that for any continuous function f , if i define a function , that is , the area under the curve between a and x right over here , that the derivative of that function is going to be f. so let me make it clear . every co... | so , in short , the derivative of the anti-derivative of a function is the original function ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | it just becomes whatever you were taking the integral of , that as a function instead of t , that is now a function x . so it can really simplify sometimes taking a derivative . and sometimes you 'll see on exams these trick problems where you had this really hairy thing that you need to take a definite integral of and... | wait , so if we are taking the derivative of an definite integral , then are we just taking the derivative of an area ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | and notice , it does n't matter what the lower boundary of a actually is . you do n't have anything on the right hand side that is in some way dependent on a . anyway , hope you enjoyed that . | is the variable t dependent upon anything at all , or is it just an arbitrary variable ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | but essentially , everywhere where you see this right over here is an f of t. everywhere you see a t , replace it with an x and it becomes an f of x . so this is going to be equal to cosine squared of x over the natural log of x minus the square root of x . you take the derivative of the indefinite integral where the u... | why put the x 's and t 's together and what 's the difference ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . | are theorems in mathematics similar to theory in physics ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | if you give me an x value that 's between a and b , it 'll tell you the area under lowercase f of t between a and x . now the cool part , the fundamental theorem of calculus . the fundamental theorem of calculus tells us -- let me write this down because this is a big deal . | whether one can prove/disprove theorem ? |
let 's say i have some function f that is continuous on an interval between a and b . and i have these brackets here , so it also includes a and b in the interval . so let me graph this just so we get a sense of what i 'm talking about . so that 's my vertical axis . this is my horizontal axis . i 'm going to label my ... | if you give me an x value that 's between a and b , it 'll tell you the area under lowercase f of t between a and x . now the cool part , the fundamental theorem of calculus . the fundamental theorem of calculus tells us -- let me write this down because this is a big deal . | is theorem a fundamental one which can be applied universally ( for example here , does fundamental theorem of calculus applicable to all functions ) ? |
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