00:01
Hello, so let's work a problem.
00:03
Our problem today is to compute the limit as x approaches 0 for x cubed over sine of x minus x.
00:14
So we start by taking the limit.
00:18
On the top, as x approaches 0, we have 0.
00:21
On the bottom, as x approaches 0, well, sine of 0 is 0 minus once more x is approaching 0.
00:29
So we have 0.
00:29
And this gives us 0 over 0.
00:33
But we have a problem here.
00:35
You can't divide by 0.
00:37
So this answer does not exist, which means that we have to take lopetal's rule.
00:45
Lopetal's rule lets us keep doing the limit so that we can find a solution to our original problem.
00:52
And to do this, we simply take the derivative at the top...