A) \[\frac{\pi }{5}\]
B) \[\frac{5}{\pi }\]
C) \[1\]
D) \[0\]
Correct Answer: A
Solution :
Since, \[f(x)\] is continuous at\[x=0\] \[\therefore \] \[\underset{x\to 0}{\mathop{\lim }}\,f(x)=f(0)\] \[\Rightarrow \] \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin \pi x}{5x}=k\] \[\Rightarrow \] \[\lim \left( \frac{\sin \pi x}{\pi x} \right)\frac{\pi }{5}=k\] \[\Rightarrow \] \[(1)\frac{\pi }{5}=k\] \[\left( \because \,\,\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin x}{x}=1 \right)\] \[\Rightarrow \] \[k=\frac{\pi }{5}\]You need to login to perform this action.
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