00:01
Here, we're given several limits we're asked to compute.
00:05
So let's start off with number 7.
00:07
If we're given something like this, what i would do first is just plug in 0.
00:12
So we have the limit as x approaches 0 of e to the x minus 1 over sine of x.
00:16
So i'm just going to plug in 0 and see what happens.
00:19
I would have e to the 0 minus 1 over the sign of 0.
00:25
Well, that e to the 0 is 1, 1 minus 1 is 0.
00:28
Sign of 0 is also 0.
00:29
I get 0 divided by 0, which is.
00:31
Is an indeterminate form.
00:33
We don't know what it is.
00:35
So that tells me that i can go ahead and apply lopatals rule.
00:39
All of that was just to tell us we can use lopatals rule.
00:43
Lopatol's rule says let's take the derivative of the top and the derivative of the bottom and the limit will not be changed.
00:49
So i'm going to have the limit as x approaches zero of the derivative of the top...