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

The correct option is D 1/6 x → 0Ltcos(sin x) cos x/x^4 = x → 0Lt sin(sin x) cos x+sin x/4x^3 =x → 0Lt cos(sin x)cos^2x+sin(sin x)sin x+cos x/12x^2 = 1/24 + 1 ...

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Byju's Answer

Standard XII

Mathematics

Using Monotonicity to Find the Range of a Function

Lttx → 0cos s...

Question

$L t x \to 0 \frac{c o s (s i n x) - c o s x}{x^{4}}$ is equal to

$\frac{1}{2}$

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$\frac{1}{6}$

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$\frac{1}{3}$

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$\frac{2}{3}$

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Solution

The correct option is B
$\frac{1}{6}$

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

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Ltx→0cos(sin x)−cos xx4 is equal to

The correct option is B 16 Ltx→0cos(sin x)−cos xx4=Ltx→0−sin(sin x) cos x+sin x4x3=Ltx→0−cos(sin x)cos2x+sin(sin x)sin x+cos x12x2=124+124+112=16

$L t x \to 0 \frac{c o s (s i n x) - c o s x}{x^{4}}$ is equal to