00:01
So we want to take this limit of x goes to 14 of f of x.
00:12
So it looks like that denominator is zero, which it is, but that doesn't mean we can actually still work with this limit.
00:25
So the numerator is x squared minus 14 squared divided by x minus 14.
00:34
And so that's the limit x goes to 14 of x minus 14 times x plus 14 divided by x minus 14.
00:48
We get to cancel the x minus 14 factor.
00:54
And so this is, so our limit is 28.
01:01
So that's l, okay? so that's actually the easier part.
01:10
So we want to find the largest delta such that zero is less than the absolute value of x minus 14 is less than delta.
01:39
So that f of x minus l is less than epsilon.
01:48
So we have an epsilon given, okay? so we'll start off with epsilon greater than f of x minus l, which is, so f, now that we've canceled out, we know that it's just x plus 14.
02:14
I'm just gonna write it that way.
02:17
So x plus 14 minus l, okay? and we know that x is within delta of being 14...