Question

pls send solution..urgent​

Answer 1

$\huge \underline \bold \green{QUESTION}: \\ \:$

$lim \small{x→1}\: { \frac{x + 1}{x + 2} }^{ \frac{1 - \sqrt{x} }{1 - x} } = ? \:$

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$\huge{ \underline{ \bold{ \orange{ \mathfrak{solution}}:}}} \: \:$

$\green{⇝} \: lim \small{x→1}\: { \frac{x + 1}{x + 2} }^{ \frac{1 - \sqrt{x} }{1 - x} } \: \\ \green{⇝} \: lim \small{x→1}\: { \frac{x + 1}{x + 2} }^{ \frac{1 - \sqrt{x} }{(1 - \sqrt{x} )(1 + \sqrt{x} )} } \: \\ \green{⇝} \: lim \small{x→1}\: { \frac{x + 1}{x + 2} }^{ \frac{1}{1 + \sqrt{x} } } \: \\ now \: substitute \: x = 1 \\ \green{⇝} \: lim \small{x→1}\: { \frac{1+ 1}{1+ 2} }^{ \frac{1}{1 + \sqrt{1} } } \\ \green{⇝} \:\: { (\frac{2}{3} )}^{ \frac{1}{2} } \\ \green{⇝} \boxed{ \sqrt{ \frac{2}{3} } }$

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$\underline\bold \red{final \: answer}$

$\: \: \: \: \: \: \: \: \red{\boxed{ \green{\sqrt{ \frac{2}{3}} } } }$

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hope this will help you

thankyou