Differentiation Question 116
Question: If $ f(x)= \begin{matrix} x^{n}\sin (1/x^{2}),x\ne 0 \\ 0,x=0 \\ \end{matrix} . $ , $ (n\in I) $ , then
Options:
A) $ \underset{x\to 0}{\mathop{\lim }}f(x) $ exists for $ n>1 $
B) $ \underset{x\to 0}{\mathop{\lim }}f(x) $ exists for $ n<0 $
C) $ \underset{x\to 0}{\mathop{\lim }}f(x) $ Does not exist for any value of n
D) $ \underset{x\to 0}{\mathop{\lim }}f(x) $ cannot be determined
Show Answer
Answer:
Correct Answer: A
Solution:
[a] for $ n>1, $
$ \underset{x\to 0}{\mathop{\lim }}x^{n}\sin (1/x^{2})=0x $ (any value between -1 and 1)=0 For n<0, $ \underset{x\to 0}{\mathop{\lim }}x^{n}\sin (1/x^{2})=\infty \times $ (any value between -1 and 1) = $ \infty $ .
BETA
