Asked by Michael
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!
lim x (arrow to the right) 1 x-1/x(squared)-1. Please help!
Answers
Answered by
Reiny
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
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.