# Thread: limit help

1. ## limit help

lim (1+tanx)^(1/2) - (1+sinx)^(1/2)
x->0 _____________________________
x3

how do you do this? the conjugate is no help!

2. ## Re: limit help

Is this \displaystyle \begin{align*} \lim_{x \to 0}\frac{\left( 1 + \tan{x} \right)^{\frac{1}{2}} - \left( 1 + \sin{x} \right)^{\frac{1}{2}}}{x^3} \end{align*}?

3. ## Re: limit help

yes so how do i go about applying the limit?
Originally Posted by Prove It
Is this \displaystyle \begin{align*} \lim_{x \to 0}\frac{\left( 1 + \tan{x} \right)^{\frac{1}{2}} - \left( 1 + \sin{x} \right)^{\frac{1}{2}}}{x^3} \end{align*}?

4. ## Re: limit help

Unfortunately, you have apparently already decided that "the conjugate is no help" and that is certainly the method I would suggest! It also helps to know the basic limit, $\lim_{x\to 0} sin(x)/x= 1$.

Or, just calculating that quantity for, say x= 0.00001 should give you a good idea.

5. ## Re: limit help

well i know the answer should be 1/4 but i still dont know how to get that or what to do?
Originally Posted by HallsofIvy
Unfortunately, you have apparently already decided that "the conjugate is no help" and that is certainly the method I would suggest! It also helps to know the basic limit, $\lim_{x\to 0} sin(x)/x= 1$.

Or, just calculating that quantity for, say x= 0.00001 should give you a good idea.