Let \[f(x)=\,\left\{ \begin{matrix} \frac{\sin \pi x}{5x}, & x\ne 0 \\ k, & x=0 \\ \end{matrix} \right.\]. If \[f(x)\] is continuous at \[x=0,\] then \[k=\] [Karnataka CET 2002]

Let \[f(x)=\,\left\{ \begin{matrix} \frac{\sin \pi x}{5x}, & x\ne

1.	Let \[f(x)=\,\left\{ \begin{matrix} \frac{\sin \pi x}{5x}, & x\ne 0 \\ k, & x=0 \\ \end{matrix} \right.\]. If \[f(x)\] is continuous at \[x=0,\] then \[k=\] [Karnataka CET 2002]
A.	\[\frac{\pi }{5}\]
B.	\[\frac{5}{\pi }\]
C.	1
D.	0
Answer» B. \[\frac{5}{\pi }\]

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Let \[f(x)=\,\left\{ \begin{matrix} \frac{\sin \pi x}{5x}, & x\ne 0 \\ k, & x=0 \\ \end{matrix} \right.\]. If \[f(x)\] is continuous at \[x=0,\] then \[k=\] [Karnataka CET 2002]

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