Functions Question 130
Question: The value of k which makes $ f(x)= \begin{cases} & \sin \frac{1}{x},\ x\ne 0 \\ & k,,x=0 \\ \end{cases} . $ continuous at $ x=0 $ is
[MNR 1995]
Options:
A) 8
B) 1
C) ?1
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
If $ x\to 0, $ then the value of $ \sin \frac{1}{x} $ passes through [?1, 1] infinitely many ways, therefore limit of the function does not exist at $ x=0. $ Hence there is no value of k for which the function is continuous at $ x=0. $
BETA
