00:01
So we want to use euler's method to help us walk through this problem, walk through the slope.
00:06
And we know that the derivative is equal to negative x over y.
00:12
And the way i like to explain it to my students is we're starting off with a point that we know at zero.
00:19
We're at the point four.
00:21
And that little should be there.
00:24
So this is what our approximation for y is.
00:28
The first one is going to be accurate.
00:29
And the rest of them are going to be approximations.
00:31
So we know we have a point right here at one, two, three, four.
00:35
We know we have that point.
00:36
And now we know the slope when we estimate for point one, we're going to think of the tangent line slope.
00:43
And we're going to walk.
00:44
We're going to start at four.
00:46
And we're going to add on a little bit of a walk.
00:50
And we're going to walk point one units on this slope.
00:54
And we're going to use this previous point of negative zero over four.
00:59
To help us figure out what that value is.
01:02
So we're going to move 0 .1 unit over, and we're going to walk that slope from that differential equation to help us find it, which means we basically are not changing our slope.
01:15
This is still going to be 4.
01:17
So we think of a new point as 0 .1 and 4 on our graph.
01:23
Now our next point, we're going to start at 4, and we're going to take a walk of half a unit to the right, and we're going to walk at this slope from the previous point.
01:36
So our slope from the previous point is 0 .1 over 4.
01:41
And so when we do that calculation, we end up getting, and let me plug that in my calculator, so i have it fresh.
01:49
And i'm also going to use some store values.
01:51
Whoops, 4 plus 0 .1 times...