Post a New Question

Calc

posted by .

I have a test soon.. and I really need to know how to do this problem.. please help!!!

lim as x-->0 sin^2(x)/tan(x^2)

the answer is 1, but I have no clue how to get that!

Use series expansions. Look up Taylor expansion on google and study that topic first.

Using series expansion techniques these limit problems become pretty trivial. For x in a neighborhood of zero:

Sin(x) = x + O(x^3) ---->

sin^2(x) = x^2 + O(x^4)

tan(x) = x + O(x^3) -->

tan(x^2) = x^2 + O(x^6)

And you see that:


sin^2(x)/tan(x^2) = 1 + O(x^4)

So, the limit is 1

Answer This Question

First Name
School Subject
Your Answer

Related Questions

More Related Questions

Post a New Question