00:01
So oftentimes theorems are incredibly useful because they allow us to take common application problems, common problems we run into in math, and be able to essentially use a formula or some theorem to simplify the idea of the problem.
00:22
So what we see in this case is we're going to want to use theorem 10 in order to find the curvature.
00:31
Of r of t being t i, t squared j plus e to the tk.
00:38
So we're going to want to write this in vector form.
00:42
I just prefer it that way.
00:43
So we'll have one, two, t, if you don't prefer it that way, you can always write it with the i's, j's, and k's, but it's really up to you.
00:54
Then we take the, oh, so that would be the first derivative right there, since this was t, this was t squared, and this was e to the t.
01:06
So our derivative, like we just said, is going to be 1, 2t, e to the t.
01:16
And then our second derivative of the vector equation is going to be 0 to e to the t.
01:26
So with this, we want to find the magnitude of the first derivative.
01:33
We see that's going to be the square root of 1 squared plus 2t squared plus e to the t squared...