00:01
This question gives us a vector field, which we must then sketch.
00:03
The vector field is equal to e to the negative x, comma, zero.
00:08
Notice that we're depending nothing on y, so that is something we're going to use when plotting it.
00:13
But before we get at this, we'll have to go ahead and draw our plane.
00:21
So if we want to look at the origin, x, 0, y, 0.
00:26
So we have e to the 0, which is 1.
00:28
So with the origin, we actually have a vector 1 comma 0.
00:32
Now let's take the point x equals 1.
00:34
We go e to the negative 1 in the x direction and 0 in the y direction.
00:41
So it's e to the negative 1 would be just a small number.
00:45
And so when we look at it, e to the negative x1 over e to the x.
00:51
As x increases, so does e to the x.
00:56
And then as the denominator increases, the actual number decreases...