00:01
Okay, first of all, let's find that limit.
00:15
If you notice, if you do a direct substitution, you are going to get a zero and a zero.
00:23
So we can do a little more work on that, and we notice that numerator can be written that way, and then we get a nice cancellation there.
00:39
Divide out.
00:42
That divides out, so we're really looking at this limit now, which is a four.
00:53
So that's our value for l.
00:56
Okay, second problem now is to find the largest delta such that if, then we will have f of x.
01:17
And you know, i'm going to use this as my new f of x because i remember when we're finding this limit, this right here, tells us we're really not concerned with what happens right at x equals 2 so that this function that we're working with here is as good as this one and the same as as long as we're not right at x equals 2 so we're gonna work with that and this back over here x plus 2 minus 4 is less than the 0 .05 okay if i simplify this one step here i get this and i got really lucky on this one because i don't have to look for any minimums.
02:07
This is the distance.
02:09
That's another way to read this is the distance from x, from 2 to x or from x to 2 is less than 0 .05...