Question

If the function f(x) = $\sqrt{2}$ is continuous at

x = 0, then the value of k is-

• A. 1
• B. –1
• C. 0
• D. e

Answer 1

Answer: (A)

1

Answer 2

$\lim _ { x \rightarrow 0 } ( \cos x ) ^ { 1 / x }$ = k ⇒ $\lim _ { x \rightarrow 0 } \frac { 1 } { x }$ log(cos x) = log k

⇒ $\lim _ { x \rightarrow 0 } \frac { 1 } { x } \lim _ { x \rightarrow 0 } \log \cos x$= log k ⇒ $\lim _ { x \rightarrow 0 } \frac { 1 } { x } \times 0$= log_ek ⇒ k = 1