(23 points) prove that the limit is correct:
lim x approaches -2 of 1/(x+1) = -1

The statement that

is equivalent to saying that, for any , there exists such that if

then it's guaranteed that

We want to pick to make this guarantee.

We have

If we assume , then

The lower bound on is what's important here, because its gives us an upper bound on the reciprocal:

Then in the expected -inequality, we have

Comparing this to our chosen -inequality, this suggests we should pick to be the smaller of and , or .

# # #

Now for the proof itself. Let be given, and assume .

and

This completes the proof.

answer: '

the distance between points l and m

step-by-step explanation:

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8