JEE Main & Advanced Mathematics Functions Question Bank Limits

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin mx}{\tan nx}=\] [DSSE 1987]

    A)                 \[\frac{n}{m}\]

    B)                 \[\frac{m}{n}\]

    C)                 \[mn\]

    D)                 None of these

    Correct Answer: B

    Solution :

                    \[\Rightarrow \,\,\underset{x\to 0}{\mathop{\lim }}\,\,\frac{x\,\left\{ 1+a\,\left( 1-\frac{{{x}^{2}}}{2\,\,!}+\frac{{{x}^{4}}}{4\,\,!}-\frac{{{x}^{6}}}{6\,\,!}+... \right) \right\}-b\,\left\{ x-\frac{{{x}^{3}}}{3\,\,!}+\frac{{{x}^{5}}}{5\,\,!}-... \right\}}{{{x}^{3}}}=1\] (formula).


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