Lim x - 11-x-2-x1-x-1-x

The correct option is C is √(23)lim_x→1(1+x2+x)^(1 √(x))/(1 x)=lim_x→1(1+x2+x)^(1 √(x))(1+√(x))/(1 x)(1+√(x)) =lim_x→1(1+x2+x)^1/(1+√(x))=(23)^1/2 ...

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Byju's Answer

Standard XII

Mathematics

Integration Using Substitution

lim x → 11+x/...

Question

$lim x \to 1 {(\frac{1 + x}{2 + x})}^{\frac{(1 - \sqrt{x})}{(1 - x)}}$

1

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does not exist

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

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ln 2

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Solution

The correct option is C is $\sqrt{\frac{2}{3}}$
$lim x \to 1 {(\frac{1 + x}{2 + x})}^{\frac{(1 - \sqrt{x})}{(1 - x)}} = lim x \to 1 {(\frac{1 + x}{2 + x})}^{\frac{(1 - \sqrt{x}) (1 + \sqrt{x})}{(1 - x) (1 + \sqrt{x})}}$
$= lim x \to 1 {(\frac{1 + x}{2 + x})}^{\frac{1}{(1 + \sqrt{x})}} = {(\frac{2}{3})}^{\frac{1}{2}}$

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limx→1(1+x2+x)(1−√x)(1−x)

The correct option is C is √23limx→1(1+x2+x)(1−√x)(1−x)=limx→1(1+x2+x)(1−√x)(1+√x)(1−x)(1+√x) =limx→1(1+x2+x)1(1+√x)=(23)12

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