# limit help

• Oct 10th 2012, 03:21 PM
pnfuller
limit help
lim (1+tanx)^(1/2) - (1+sinx)^(1/2)
x->0 _____________________________
x3

how do you do this? the conjugate is no help!
• Oct 10th 2012, 06:15 PM
Prove It
Re: limit help
Is this \displaystyle \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*}?
• Oct 11th 2012, 08:37 AM
pnfuller
Re: limit help
yes so how do i go about applying the limit?
Quote:

Originally Posted by Prove It
Is this \displaystyle \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*}?

• Oct 11th 2012, 11:56 AM
HallsofIvy
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, $\displaystyle \lim_{x\to 0} sin(x)/x= 1$.

Or, just calculating that quantity for, say x= 0.00001 should give you a good idea.
• Oct 11th 2012, 12:16 PM
pnfuller
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?
Quote:

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, $\displaystyle \lim_{x\to 0} sin(x)/x= 1$.

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