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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2008

  • question_answer
    \[\underset{x\to \infty }{\mathop{\lim }}\,\,x\,\sin \left( \frac{2}{x} \right)\] is equal to

    A)  \[\infty \]                                          

    B)  \[0\]

    C)  \[2\]                                    

    D)  \[\frac{1}{2}\]

    Correct Answer: C

    Solution :

    \[\underset{x\to \infty }{\mathop{\lim }}\,\,x\sin \left( \frac{2}{x} \right)=\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin \left( \frac{2}{x} \right)}{\frac{1}{2}\left( \frac{2}{x} \right)}=2\]


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