If the function `f(x)={(cosx)^(1/x),x!=0k ,x=0` is continuous at `x=0` , then the value of `k` is `(a)0` (b) `1` (c) `-1` (d) `e`

Explanation

To determine the value of \( k \) such that the function

\[
f(x) =
\begin{cases}
(\cos x)^{\frac{1}{x}}, & x \neq 0 \\
k, & x = 0
\end{cases}
...