Let \[f(x)=\left\{ \begin{matrix} x\sin \left( \frac{1}{x} \right)+\sin \left( \frac{1}{{{x}^{2}}} \right),x\ne 0 \\ 0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\ \end{matrix} \right.\]then \[\underset{x\to \infty }{\mathop{\lim }}\,f(x)\] equals

Let \[f(x)=\left\{ \begin{matrix} x\sin \left( \frac{1}{x} \right)+\s

1.	Let \[f(x)=\left\{ \begin{matrix} x\sin \left( \frac{1}{x} \right)+\sin \left( \frac{1}{{{x}^{2}}} \right),x\ne 0 \\ 0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\ \end{matrix} \right.\]then \[\underset{x\to \infty }{\mathop{\lim }}\,f(x)\] equals
A.	0
B.	\[-1/2\]
C.	1
D.	None of these
Answer» D. None of these

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Let \[f(x)=\left\{ \begin{matrix} x\sin \left( \frac{1}{x} \right)+\sin \left( \frac{1}{{{x}^{2}}} \right),x\ne 0 \\ 0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\ \end{matrix} \right.\]then \[\underset{x\to \infty }{\mathop{\lim }}\,f(x)\] equals

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