Split (1)

train · 116k rows

role stringclasses 2 values	content stringlengths 0 2.1k	session_id int64 10 21.7k	sequence_id int64 0 2.38k	annotations listlengths 0 8
volunteer	over the change in X.	16,993	148	[]
volunteer	2 minus X1.	16,993	149	[]
volunteer	And we know, and we can say	16,993	150	[]
volunteer	that it's F(X2)	16,993	151	[]
volunteer	minus FOX1 because Y1 is just equal to F of X1.	16,993	152	[]
volunteer	over X2.	16,993	153	[]
volunteer	minus X1	16,993	154	[]
volunteer	right? So now the question becomes	16,993	155	[]
volunteer	um, what is F of X2.	16,993	156	[]
volunteer	And how is it related	16,993	157	[]
volunteer	to X1? Can we use X1 to approximate F of X2 if we don't know what F of X is.	16,993	158	[]
volunteer	right? Like the only, the only information we have about FFX	16,993	159	[]
volunteer	is the point X1F of X1.	16,993	160	[]
volunteer	and that it's occur and then we have a tangent line.	16,993	161	[]
volunteer	That's the only information we have about the function F	16,993	162	[]
volunteer	Um, and knowing that we want to know, is there, is it possible to find the value F of X2.	16,993	163	[]
volunteer	OK.	16,993	164	[]
volunteer	So going back to this equation, we say FX2 what is is equal to FFX1, which is just, you know, Y1	16,993	165	[]
volunteer	We're saying plus some uh delta X	16,993	166	[]
volunteer	times	16,993	167	[]
volunteer	the slope	16,993	168	[]
volunteer	which really is just some kind of	16,993	169	[]
student	ok ok	16,993	170	[]
volunteer	right, which really this, this is actually just some kind of like error function.	16,993	171	[]
student	ohhh	16,993	172	[]
volunteer	right? Because we know that um	16,993	173	[]
volunteer	that	16,993	174	[]
volunteer	Y2 cannot equal F of X2.	16,993	175	[]
volunteer	because the definition of a tangent line	16,993	176	[]
volunteer	means that it only intersects the function at one point.	16,993	177	[]
volunteer	So by definition, Y2 can't, there can't be a second	16,993	178	[]
volunteer	point	16,993	179	[]
volunteer	that the tangent line touches on the function because by that point, it wouldn't be a tangent line anymore. It'd be a secant line.	16,993	180	[]
student	yeah	16,993	181	[]
volunteer	right	16,993	182	[]
volunteer	So, um	16,993	183	[]
volunteer	and what what happens is, is that if you can approximate	16,993	184	[]
volunteer	this delta X, if you take whatever step you have, you would find that, um, let's say F of X2	16,993	185	[]
volunteer	is equal to Y1, right? The, the point we know about the, the height of the point we know about, plus some	16,993	186	[]
volunteer	uh	16,993	187	[]
volunteer	I'm sorry, let me do that again. This is actually	16,993	188	[]
volunteer	not Y2. This would be Y1, right? So you say FFX2 because we know what F of X1 is in relation to why we can approximate say FFX2 is equal to Y2, let's say plus some error value.	16,993	189	[]
volunteer	right? Cause we know Y2 can't equal XF X2.	16,993	190	[]
volunteer	but if we, depending on how big our delta X is, we know that we can, um, kind of approximate	16,993	191	[]
volunteer	this value. This in all this right here is just an approximation.	16,993	192	[]
volunteer	right? Because we want to know what is this error value?	16,993	193	[]
volunteer	And we say it's an error value because we know, um, if you look back at the graph	16,993	194	[]
volunteer	right, we have Y2 here.	16,993	195	[]
volunteer	and this is F of X2, and you see there's this gap here.	16,993	196	[]
volunteer	right?	16,993	197	[]
volunteer	And that gap	16,993	198	[]
volunteer	I'm sorry, that's not a plus, it should be a minus then.	16,993	199	[]
volunteer	Uh	16,993	200	[]
volunteer	I guess it doesn't really matter	16,993	201	[]
volunteer	Yeah, it's, it's a minus	16,993	202	[]
volunteer	I guess the sign doesn't really matter because it could just be a negative value.	16,993	203	[]
volunteer	But basically, we want to know what is um	16,993	204	[]
volunteer	what is this error value	16,993	205	[]
volunteer	right? What is this gap between Y2 and X2.	16,993	206	[]
volunteer	And the, and the problem becomes if this gap	16,993	207	[]
volunteer	is too big	16,993	208	[]
volunteer	then we really have no idea what F of X2.	16,993	209	[]
volunteer	is.	16,993	210	[]
volunteer	right? Approximation could be way off.	16,993	211	[]
volunteer	And this is, this happens when um	16,993	212	[]
volunteer	this gap between X2 and X1. By the way, I didn't, I didn't explain this, but Delta X is just equal to um the difference between two points of X. So it'll be X2 minus X1, or it could just be XI + 1 minus XI, right?	16,993	213	[]
volunteer	That's just what Delta X just means there's a difference.	16,993	214	[]
volunteer	We're just comparing um the distance between two x values in this instance.	16,993	215	[]
volunteer	OK.	16,993	216	[]
volunteer	Does that make sense so far	16,993	217	[]
student	yes	16,993	218	[]
volunteer	I know I'm going, I'm kind of going back and repeating um information you might have already known.	16,993	219	[]
volunteer	Um	16,993	220	[]
volunteer	so, right, so we want to figure out	16,993	221	[]
student	no no its very helpful	16,993	222	[]
volunteer	so we've solved for the error value, we find that um Y2 is that the error values you go to Y1 minus	16,993	223	[]
volunteer	F of X2	16,993	224	[]
volunteer	right?	16,993	225	[]
volunteer	And we can also say	16,993	226	[]
volunteer	that Y2	16,993	227	[]
volunteer	or sorry, Y of X2.	16,993	228	[]
volunteer	is equal to	16,993	229	[]
volunteer	M of	16,993	230	[]
volunteer	X2 minus X1.	16,993	231	[]
volunteer	plus Y1 based based on our uh tangent line	16,993	232	[]
volunteer	right, which we have up here.	16,993	233	[]
volunteer	right? All I did was plug in X2 for X.	16,993	234	[]
volunteer	OK.	16,993	235	[]
volunteer	But we also know that X2 minus X1 is the same as delta X, right?	16,993	236	[]
volunteer	So we find that M times delta x	16,993	237	[]
volunteer	+ Y1	16,993	238	[]
volunteer	is equal to YX2	16,993	239	[]
volunteer	So what they're saying is that Y2 is just equal to Y1	16,993	240	[]
volunteer	plus the slope, right, the change.	16,993	241	[]
volunteer	times the change in X	16,993	242	[]
volunteer	which we also know that the slope M	16,993	243	[]
volunteer	is just equal to deltay over delta X.	16,993	244	[]
volunteer	right, which we found up here	16,993	245	[]
volunteer	Oh, I'm sorry, the Y2 here.	16,993	246	[]
volunteer	Yeah, I was a little ugly. Let me, um, you're correct, that is supposed to be Y2. The Y2 cannot equal X2	16,993	247	[]

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