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December 22, 2014

December 22, 2014

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

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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