Differentiation Question 130
Question: Let $ f(x)= \begin{matrix} x\sin ( \frac{1}{x} )+\sin ( \frac{1}{x^{2}} ),x\ne 0 \\ 0,x=0 \\ \end{matrix} . $ then $ \underset{x\to \infty }{\mathop{\lim }}f(x) $ equals
Options:
A) 0
B) $ -1/2 $
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ \underset{x\to \infty }{\mathop{\lim }}f(x)=\underset{x\to \infty }{\mathop{\lim }}x\sin ( \frac{1}{x} )+\sin ( \frac{1}{x^{2}} ) $
$ =\underset{x\to \infty }{\mathop{\lim }}\frac{\sin ( \frac{1}{x} )}{( \frac{1}{x} )}+\underset{x\to \infty }{\mathop{\lim }}\sin ( \frac{1}{x^{2}} )=1+0=1. $
BETA
