00:02
Okay, let's do the second one first.
00:05
Here's a picture of the sign of x.
00:08
Here's pi.
00:09
Here's two pi.
00:15
You can see that as x approaches zero, this function goes to y equals zero.
00:21
So the top is zero.
00:24
And then here's e to the x.
00:26
As x approaches zero, that goes to one, right there.
00:30
Zero over one, that's zero.
00:34
Okay, so that one won bad.
00:35
This one, however, is a much horror problem.
00:39
So the strategy is first to set it equal to something.
00:44
So y is always a good thing.
00:49
Okay, the reason why this one is harder than the other one is because you have an x up in the exponent and an x in the base.
00:58
Okay, and the only way to get these two things separated from each other is by taking the logarithm.
01:04
Oh, and the reason we have to do it is because we have zero to the zero power, which is indeterminate.
01:11
So what i'm going to do is i'm going to take the natural log of both sides.
01:15
And when you take the log of the limit, it's the same as the limit of the log.
01:19
So you can move the limit out here and take the log of this stuff on the inside like this.
01:30
Okay, now what you do is you use the logarithm rule, which says you can bring the exponent out into the front.
01:38
So now we have lny equals, but not out front of the limit, but out front of the logarithm.
01:47
So now we have sine x times lnx.
01:54
Okay, so if you plug zero in here, you get zero times...