00:01
In part a, we're asked to sketch the graph of y equals e to the x as a curve in r2.
00:10
So this is a pretty standard graph.
00:14
We have our x and y axes, which intersect at the origin.
00:20
And we have that there is a y intercept at y equals 1.
00:26
There is an asymptote of y equals 0 as x approaches negative infinity.
00:32
And the function approaches positive infinity as x approaches infinity.
00:37
And so our function looks like this, y equals e to the x.
00:52
In part b, we're asking to sketch a graph of y equals e to the x as a surface in r3.
00:58
I'll notice that the equation y equals e to the x doesn't involve the third variable z.
01:10
The horizontal traces are copies of the curve y equals e to the x.
01:27
And the rulings are parallel to the x -axis.
01:29
So to sketch this first, let's draw our x, y, and z plane, x, y, z space.
01:50
So we have our x, y, and z axes.
02:08
And first we'll just draw our curve y equals y in the xy plane.
02:13
So as we know, we have an intercept, a y intercept of about one.
02:17
And then as x approaches negative infinity, the curve approaches zero...