lim _{x rightarrow 1}left(frac{1+x}{2+x}right | vedclass

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(C) We have, $\lim _{x \rightarrow 1}\left(\frac{1+x}{2+x}\right)^{\frac{1-\sqrt{x}}{1-x}}$$= \lim _{x \rightarrow 1}\left(\frac{1+x}{2+x}\right)^{\fr

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$\sqrt{\frac{2}{3}}$

Vedclass · Answer

(C) We have, $\lim _{x \rightarrow 1}\left(\frac{1+x}{2+x}\right)^{\frac{1-\sqrt{x}}{1-x}}$$= \lim _{x \rightarrow 1}\left(\frac{1+x}{2+x}\right)^{\frac{1-\sqrt{x}}{(1+\sqrt{x})(1-\sqrt{x})}}$$= \lim _{x \rightarrow 1}\left(\frac{1+x}{2+x}\right)^{\frac{1}{1+\sqrt{x}}}$$= \left(\frac{1+1}{2+1}\right)^{\frac{1}{1+1}} = \left(\frac{2}{3}\right)^{\frac{1}{2}} = \sqrt{\frac{2}{3}}$

$\lim _{x \rightarrow 1}\left(\frac{1+x}{2+x}\right)^{\frac{1-\sqrt{x}}{1-x}}$ is equal to

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