The correct option is B 1 lim_x→ 0 ( sin x/x )^1/x , nbsp; nbsp; nbsp; nbsp; [1^∞ form ] =lim_x→ 0 (1+ sin x x/x )^x/sin x x.sin x x/x^2 ...

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Definite Integral as Limit of Sum

limx→ 0 sin x...

Question

$lim x \to 0 {(\frac{sin x}{x})}^{1 / x}$

-1

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Solution

The correct option is B 1
$lim x \to 0 {(\frac{sin x}{x})}^{1 / x}$ , $[1^{\infty}$ form ]
$= lim x \to 0 {(1 + \frac{sin x - x}{x})}^{\frac{x}{sin x - x} . \frac{sin x - x}{x^{2}}}$
$= e^{lim x \to 0 \frac{(x - x^{3} / 3 + . . . . . . . . .) - x}{x^{2}}} = e^{0} = 1$

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