JEE Main & Advanced Mathematics Functions Question Bank Limits

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin (2+x)-\sin (2-x)}{x}=\]                 [AI CBSE 1983; AISSE 1982, 83]

    A)                 \[\sin 2\]

    B)                 \[2\sin 2\]

    C)                 \[2\cos 2\]

    D)                 2

    Correct Answer: C

    Solution :

                       Apply formula of \[\sin C-\sin D\],            i.e., \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin (2+x)-\sin (2-x)}{x}=\underset{x\to 0}{\mathop{\lim }}\,\frac{2\cos 2.\sin x}{x}\]                                 \[L\,{g}'(0)=0\]                 You may also apply L-Hospital rule.


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