A) 0
B) \[-1/2\]
C) 1
D) None of these
Correct Answer: C
Solution :
[c] \[\underset{x\to \infty }{\mathop{\lim }}\,f(x)=\underset{x\to \infty }{\mathop{\lim }}\,x\sin \left( \frac{1}{x} \right)+\sin \left( \frac{1}{{{x}^{2}}} \right)\] \[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{\sin \left( \frac{1}{x} \right)}{\left( \frac{1}{x} \right)}+\underset{x\to \infty }{\mathop{\lim }}\,\sin \left( \frac{1}{{{x}^{2}}} \right)=1+0=1.\]
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