Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Lim x->1 (sin (x^2 - 1) / (x-1)?
I need to see the step by step work for this. I looked it up on wolfram alpha, and it says the limit is 2, but we haven't learned L'Hospital's rule yet, so I can't use the step by step on wolfram alpha. Could you help please?
1 Answer
- kbLv 79 years agoFavorite Answer
Use lim(t→0) sin(t)/t = 1 as follows:
lim(x→1) sin(x^2 - 1)/(x - 1)
= lim(x→1) (x + 1) * sin(x^2 - 1)/[(x + 1) * (x - 1)]
= lim(x→1) (x + 1) * sin(x^2 - 1)/(x^2 - 1)
= lim(x→1) (x + 1) * lim(x→1) sin(x^2 - 1)/(x^2 - 1)
= lim(x→1) (x + 1) * lim(t→0) sin(t)/t, letting t = x^2 - 1
= 2 * 1
= 2.
I hope this helps!
