The value of lim x - 0sin x1-x-1 - xsin x where x-0 is

The correct option is C 1lim_x→ 0(sin x)^1/x+ ( 1/x )^sin x =lim_x→ 0(sin x)^1/x+lim_x→ 0 ( 1/x )^sin x =0+e^lim_x→ 0sin x ln1/x =e^lim_x→ 0 ln(x)/cosec x ...

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Byju's Answer

Standard XII

Mathematics

L'Hospital Rule to Remove Indeterminate Form

The value of ...

Question

The value of ${lim}_{x \to 0} ((s i n x)^{\frac{1}{x}} + (1 / x)^{s i n x})$ where $x > 0$ is

-1

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Solution

The correct option is B 1
${lim}_{x \to 0} (s i n x)^{\frac{1}{x}} + {(\frac{1}{x})}^{s i n x} = {lim}_{x \to 0} (s i n x)^{\frac{1}{x}} + {lim}_{x \to 0} {(\frac{1}{x})}^{s i n x} = 0 + e^{{lim}_{x \to 0} s i n x l n \frac{1}{x}} = e^{{lim}_{x \to 0} \frac{- l n (x)}{c o s e c x}} = e^{{lim}_{x \to 0} \frac{- \frac{1}{x}}{- c o s e c x c o t x}} = e^{{lim}_{x \to 0} \frac{s i n x}{x} . t a n x} = e^{0} = 1$

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The value of limx→0((sin x)1x+(1/x)sin x) where x>0 is

The correct option is B 1limx→0(sin x)1x+(1x)sin x=limx→0(sin x)1x+limx→0(1x)sin x=0+elimx→0sin xln1x=elimx→0−ln(x)cosecx=elimx→0−1x−cosecx cot x=elimx→0sin xx.tanx=e0=1

The value of ${lim}_{x \to 0} ((s i n x)^{\frac{1}{x}} + (1 / x)^{s i n x})$ where $x > 0$ is