Lim x - 0cos sin x-cos x-x4 is equal to

The correct option is B 1/6 lim_x → 0cos(sinx) cosx/x^4=lim_x → 0 sin(sinx)cosx+sinx/4x^3 = lim_x → 0 cos(sinx)cos^2x+sin(sinx)+cosx/12x^2= 1/24+1/24+1/12=1/ ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x → 0cos ...

Question

${lim}_{x \to 0} \frac{c o s (s i n x) - c o s x}{x^{4}} i s e q u a l t o$

1/2

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Solution

The correct option is B
1/6

${lim}_{x \to 0} \frac{c o s (s i n x) - c o s x}{x^{4}} = {lim}_{x \to 0} \frac{- s i n (s i n x) c o s x + s i n x}{4 x^{3}} = {lim}_{x \to 0} \frac{- c o s (s i n x) c o s^{2} x + s i n (s i n x) + c o s x}{12 x^{2}} = \frac{1}{24} + \frac{1}{24} + \frac{1}{12} = \frac{1}{6}$

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limx→0cos(sinx)−cosxx4 is equal to

The correct option is B 1/6 limx→0cos(sinx)−cosxx4=limx→0−sin(sinx)cosx+sinx4x3=limx→0−cos(sinx)cos2x+sin(sinx)+cosx12x2=124+124+112=16

${lim}_{x \to 0} \frac{c o s (s i n x) - c o s x}{x^{4}} i s e q u a l t o$