If $f(x)=\left\{\begin{matrix}\frac{sin \pi x}{5x}, & x≠0\\k , & x=0 \end{matrix}\right. $ is continuous at x =0, then k is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{\pi }{5}$
$f(0)=k$
$\underset{x→0}{\lim}\frac{\sin πx}{5(πx)}×π=\frac{π}{5}=k$