JEE Main & Advanced Mathematics Functions Question Bank Limits

  • question_answer
    \[\underset{\theta \to 0}{\mathop{\lim }}\,\frac{1-\cos \theta }{{{\theta }^{2}}}=\] [AI CBSE 1981, 91; DSSE 1981, 83]

    A)                 1

    B)                 2

    C)                 \[\frac{1}{2}\]

    D)                 \[\frac{1}{4}\]

    Correct Answer: C

    Solution :

                       \[\underset{\theta \to 0}{\mathop{\lim }}\,\,\frac{2\,{{\sin }^{2}}(\theta /2)}{{{\theta }^{2}}}=\frac{1}{2}.\]                 Aliter : Apply L-Hospital?s rule.


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