Functions Question 354
Question: Let $ f(x)=, \begin{cases} \frac{\sin \pi x}{5x}, & x\ne 0 \\ k, & x=0 \\ \end{cases} . $ . If $ f(x) $ is continuous at $ x=0, $ then $ k= $
[Karnataka CET 2002]
Options:
A) $ \frac{\pi }{5} $
B) $ \frac{5}{\pi } $
C) 1
D) 0
Show Answer
Answer:
Correct Answer: A
Solution:
Since $ f(x) $ is continuous at $ x=0, $ therefore $ \underset{x\to 0}{\mathop{lim}},f(x)=f(0) $
Þ $ \underset{x\to 0}{\mathop{lim}},\frac{\sin \pi ,x}{5x}=k $
Þ $ \underset{x\to 0}{\mathop{lim}},( \frac{\sin \pi ,x}{\pi x} ),.,\frac{\pi }{5}=k $
Þ $ (1),.,\frac{\pi }{5}=k $
Þ $ k=\frac{\pi }{5} $ .
BETA
