Solve lim x- 0 1-x co x

The correct option is A e lim_x→ 0(1+x)^cosec x 1^∞ formAns e^L Where L=lim_x→ 0(1+x 1) cosec x= lim_x→ 0x/sin x=1 #160; ...

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Standard XII

Mathematics

Integration as Antiderivative

Solve lim x...

Question

Solve ${lim}_{x \to 0} {(1 + x)}^{c o sec x}$

e

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e^{2}

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e^{3}

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e^{4}

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Solution

The correct option is A $e$
${lim}_{x \to 0} (1 + x)^{c o s e c x}$
$1^{\infty}$ form
Ans $e^{L}$
Where $L = {lim}_{x \to 0} (1 + x - 1)$ cosec x
= ${lim}_{x \to 0} \frac{x}{s i n x} = 1$
$∴$ Ans =e

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Solve limx→0(1+x)cosecx

The correct option is A elimx→0(1+x)cosecx1∞ formAns eLWhere L=limx→0(1+x−1) cosec x=limx→0xsinx=1 ∴ Ans =e

Solve ${lim}_{x \to 0} {(1 + x)}^{c o sec x}$

The correct option is A $e$
${lim}_{x \to 0} (1 + x)^{c o s e c x}$
$1^{\infty}$ form
Ans $e^{L}$
Where $L = {lim}_{x \to 0} (1 + x - 1)$ cosec x
= ${lim}_{x \to 0} \frac{x}{s i n x} = 1$
$∴$ Ans =e