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

## Answer This Question

## Related Questions

- Calc - Use a table of values to estimate the value of the limit. lim (tan 3x/tan...
- Math - help really needed - I'm sorry to double post; I don't want to seem ...
- Math - help really needed - Prove each idenity. 1+1/tan^2x=1/sin^2x 1/cosx-cosx=...
- Calculus - Below are the 5 problems which I had trouble in. I can't seem to get ...
- calculus - f(x)= 3x+2, x<0 3, x=0 x^2+1, x>0 g(x)= -x+3, x<1 0, x=1 x^2...
- CALCULUS - need help! - Determine the limit of the trigonometric function (if it...
- Maths- complex numbers - Find tan(3 theta) in terms of tan theta Use the formula...
- Calculus-Limits - Okay, i posted this question yesterday, however, I did not ...
- calc bc (condensed - is the limit as x approaches 0 of sin3x over 3x equal to ...
- math - Using taylor series solve lim x→0 ((sin^-1 6x)-(sin 6x))/((tan^-1)(...

More Related Questions