lim x → 0 ( cos x ) 1 / x 4 Options: A . &nbsp0 B . &nbsp1 C . &nbspe D . &nbsplimit does not exist

Answer: Option A : A lim x → 0 ( cos x ) 1 / x 4 = e lim x → 0 cos x − 1 x 4 e lim x → 0 − 2 sin x 2 x 2 . sin x 2 x 2 × 1 4 x 2 = e − ∞ = 0

limx→0(cosx)1/x4

Question

lim x \to 0 (cos x)^{1 / x^{4}}

Options:

A . 0

B . 1

C . e

D . limit does not exist

Answer: Option A
:
A

lim x \to 0 (cos x)^{1 / x^{4}} = e^{lim x \to 0} \frac{cos x - 1}{x^{4}}

e^{lim x \to 0} \frac{- 2 sin \frac{x}{2}}{\frac{x}{2}} . \frac{sin \frac{x}{2}}{\frac{x}{2}} \times \frac{1}{4 x^{2}} = e^{- \infty} = 0

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