$\displaystyle \lim_{x \to 0} \frac{(1+x)^{1/3} (\sqrt{4+x} -1) - \sqrt{1-x}}{4 x}$
Last edited by mr fantastic; Jun 9th 2010 at 09:29 PM. Reason: Fixed latex, re-titled.
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Originally Posted by bgbgbgbg $\displaystyle lim_(x->0) ((1+x)^(1/3) (sqrt(4+x)-1)-sqrt(1-x))/(4 x$) is this what you mean? $\displaystyle \lim_{x \to 0} \frac{(1+x)^{\frac{1}{3}} [(\sqrt{4+x}-1)-\sqrt{1-x}]}{4x}$
Last edited by skeeter; Jun 6th 2010 at 05:45 AM.
Hello, bgbgbgbg! I think you meant: .$\displaystyle \lim_{x\to0} \frac{(1+x)^{1/3} (\sqrt{4+x}-1)-\sqrt{1-x}}{4x}$ . . But it doesn't matter . . . Plug in $\displaystyle x = 0$ and see what you get.
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