Find the values of k so that the function f is continuous at the indicated point in`f(x)={{:((kcosx)/(pi-2x), ifx!=pi/2 ),(3, ifx=pi/2):}` at `x=pi/2`

Explanation

To determine the values of \( k \) that make the function \( f(x) \) continuous at \( x = \frac{\pi}{2} \), we need to ensure that the limit of \( f(x) \) as \( x \) approaches \( \frac{\pi}{2} \) is equal to the value of the function at that point, which is \( f\left(\frac{\pi}{2}\right) = 3 \).

The function is defined as:
\[
f(x) =
\begin{cases}
\frac{k \cos x}{\pi - 2x} & \text{if } x \neq \frac{\pi}{2} \\
3 & \text{if } x = \frac{\pi}{2}
...