Lim x - 0sin x-xsin x-x-sin x equals

The correct option is B e 1 lim_x→ 0 (sin x/x )^ (sin x/x sin x ) (form 1^∞) = e^ lim_x→ 0 (sin x/x 1 ) sin x/(x sin x) = e^ lim_x→ 0 sin x/x = e^1 ...

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Byju's Answer

Standard XI

Mathematics

L'Hospital Rule to Remove Indeterminate Form

lim x → 0sin ...

Question

$lim x \to 0 {(\frac{s i n x}{x})}^{(\frac{s i n x}{x - s i n x})}$ equals

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e^-1

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e^-2

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Solution

The correct option is C
e^-1

$lim x \to 0 {(\frac{s i n x}{x})}^{(\frac{s i n x}{x - s i n x})}$ $(f o r m 1^{\infty})$

= $e^{- lim x \to 0 (\frac{s i n x}{x} - 1) \frac{s i n x}{(x - s i n x)}}$
= $e^{- lim x \to 0 \frac{- s i n x}{x}}$
= $e^{1}$

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Similar questions

lim x \to 0 {(\frac{sin x}{x})}^{\frac{sin x}{x - sin x}} =

Q. Then value of

lim x \to 0 {(\frac{sin x}{x})}^{\frac{sin x}{x - sin x}}

Q. The value of

e ⎡ ⎢ ⎢ ⎣ lim x \to 0 {(\frac{sin x}{x})}^{\frac{sin x}{x - sin x}} + lim x \to 1 x^{\frac{1}{1 - x}} ⎤ ⎥ ⎥ ⎦

Q. Evaluate:

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, then the value of

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limx→0(sin xx)(sin xx−sin x) equals

The correct option is C e-1 limx→0(sin xx)(sin xx−sin x) (form 1∞) = e−limx→0(sin xx−1)sin x(x−sin x) = e−limx→0−sin xx = e1

$lim x \to 0 {(\frac{s i n x}{x})}^{(\frac{s i n x}{x - s i n x})}$ equals

The correct option is C
e^-1

$lim x \to 0 {(\frac{s i n x}{x})}^{(\frac{s i n x}{x - s i n x})}$ $(f o r m 1^{\infty})$

= $e^{- lim x \to 0 (\frac{s i n x}{x} - 1) \frac{s i n x}{(x - s i n x)}}$
= $e^{- lim x \to 0 \frac{- s i n x}{x}}$
= $e^{1}$