​ The value of k for which f(x) = (sin 5x/3x, if x ≠ 0) (k, if x = 0) is continuous at x = 0 is ​A. 1/3 B. 0 C. 3/5 D.5/3

Question

The value of k for which f(x) = \(\begin{cases} \frac{sin\,5x}{3x}, & if\,x\neq0 \\ k, & if\,x=0 \end{cases}\) is continuous at x = 0 is

sin 5x/3x, if x ≠ 0

k, if x = 0

A. 1/3

B. 0

C. 3/5

D.5/3

Answer 1

Answer is: D. 5/3

Since f(x) is continuous on 0.