Question

I'm in Calculus AP and we are learning about limits. I'm having trouble with finding limits algebraically. So here's a sample that you can use to help explain this to me. Find the limit of
lim x (arrow to the right) 1 x-1/x(squared)-1. Please help!

Answer 1

In any algebraic limit, proceed as follows
1. sub in the approaching value , in this case x = 1, into the expression.
2. If you get a real number, that is your answer. You are done
3. If you get a/0, where a ≠ 0, then your limit is undefined, or "there is no limit"
4. If you get 0/0, then your expression will somehow factor and you will be able to reduce it.

in this case we get 0/0 , so let's look for factoring.
Sure enough,
Limit (x-1)/(x^2-1)
= limit (x-1)/[(x-1)(x+1)] as x-->1
= limit 1/(x+1) , as x ---> 1
= 1/(1+1)
= 1/2