lim (1+tanx)^(1/2) - (1+sinx)^(1/2)

x->0 _____________________________

x^{3 how do you do this? the conjugate is no help!}

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- Oct 10th 2012, 03:21 PMpnfullerlimit help
lim (1+tanx)^(1/2) - (1+sinx)^(1/2)

x->0 _____________________________

x^{3 how do you do this? the conjugate is no help!} - Oct 10th 2012, 06:15 PMProve ItRe: 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 AMpnfullerRe: limit help
- Oct 11th 2012, 11:56 AMHallsofIvyRe: 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 PMpnfullerRe: limit help