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April 20, 2014

Homework Help: Calc

Posted by Urgent on Friday, March 30, 2007 at 2:30pm.

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

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