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[ngminhtuan]

$\lim_{x\rightarrow -1}\frac{\sqrt{\pi }-\sqrt{arccosx}}{\sqrt{x+1}}$

[dark templar]

$\lim_{x\rightarrow -1}\frac{\sqrt{\pi }-\sqrt{arccosx}}{\sqrt{x+1}}$

Theo Lopitan :
$$\lim_{x \to -1}\dfrac{\sqrt{\pi}-\sqrt{\arccos x}}{\sqrt{x+1}}=\lim_{x \to -1}\dfrac{\dfrac{1}{2\sqrt{1-x^2}\sqrt{\arccos x}}}{\dfrac{1}{2\sqrt{x+1}}}=\lim_{x \to -1}\dfrac{1}{\sqrt{1-x}\sqrt{\arccos x}}=\dfrac{1}{\sqrt{2\pi}}$$

Edited by dark templar, 02-01-2013 - 20:22.