Question

For what value of k, the following function is continuous at x = 0?

\(f(x) = \begin{cases} \frac{1-cos4x}{8x^2}&, & \quad x≠0\\ k&, & \quad x=0 \end{cases}\)

Answer 1

Given function,

\(f(x) = \begin{cases} \frac{1-cos4x}{8x^2}&, & \quad x≠0\\ k&, & \quad x=0 \end{cases}\) 

At x = 0,

We have f(0) = k

For f(x) to be continuous at x = 0

⇒ 1 = I = k

∴ k = 1