Functions Question 252
Question: If $ f(x)= \begin{cases} & x\sin \frac{1}{x},x\ne 0 \\ & k,x=0 \\ \end{cases} . $ is continuous at $ x=0 $ , then the value of k is
[MP PET 1999; AMU 1999; RPET 2003]
Options:
A) 1
B) ?1
C) 0
D) 2
Show Answer
Answer:
Correct Answer: C
Solution:
If function $ f(x) $ is continuous at $ x=0, $ then $ f(0)=\underset{x\to 0}{\mathop{\lim }}f(x) $ Given $ f(0)=k $ ; $ f(0)=k=\underset{x\to 0}{\mathop{\lim }}x,( \sin \frac{1}{x} ) $ $ f(0)=k=0,\text{ }( -1\le \sin \frac{1}{x}\le 1 ) $ ;
$ \therefore ,k=0 $ ..
BETA
