For what value of k is the function f(x) = {[sin 2x/x,x ≠ 0][k,x=0] continuous at x = 0? ​

Question

For what value of k is the function \(f(x) = \begin{cases}\frac{sin\,2x}{x}&, \quad x≠0\\k &, \quad\,\,x=0\\\end{cases} \)

continuous at x = 0?

Answer 1

For f(x) to be continuous at x = 0, 

f(0)^– = f(0)⁺ = f(0)

Since, 

f(0)^– = f(0) + = f(0) 

k = 2