00:01
Okay, so here we want to prove that the limit as x approaches negative 2.
00:14
F of x is 4, where f of x is going to be x squared almost everywhere, long as x is not negative 2, and it's going to be 1.
00:33
X equals negative 2.
00:36
Okay, so again i want to start with an epsilon bigger than 0, and actually, we're not even interested when x is equal to negative 2.
00:44
So we can really ignore the second part of the function.
00:46
We're just concerned when x is near negative 2, but not equal to negative 2.
00:52
So we want for when x plus 2, let's see, we want to find a delta.
01:01
So given an epsilon gradient 0, we want to find a delta such that when absolute value of x plus 2 is less than delta, x squared minus 4.
01:15
Is less than epsilon.
01:21
All right, great.
01:25
So what we want to do here is first, of course, note that let's see, x plus 2 is between delta and minus delta.
01:41
And so over here, well this is a little bit tricky, but we can actually factor this.
01:48
So this is going to be x plus 2 times x minus 2 okay and that's less than epsilon right and so the first thing we can do is uh well so we have this x so we're we're close right so we have this x plus 2 which we know is between minus delta and delta we're going to require but we're multiplying by this x minus 2.
02:20
So we actually need a bound on x minus 2...