Question

The limiting value of (cos x)^{1/sin x} as x → 0 is –

• A. 1
• B. e
• C. 0
• D. None of these

Answer 1

Answer: (A)

1

Answer 2

Put cos x = 1 + y as ; x → 0 ; y → 0

Hence $\lim _ { x \rightarrow 0 }$(cos x)^{1/sin x} = $\lim _ { y \rightarrow 0 }$ [(1 + y)^1/y]^{y/sin x}

$\mathrm { e } ^ { \lim _ { \mathrm { x } \rightarrow 0 } \frac { \cos \mathrm { x } - 1 } { \sin \mathrm { x } } }$ = = e⁰ = 1.

Hence (1) is the correct answer.