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  3. RAJASTHAN ­ PET

RAJASTHAN ­ PET Rajasthan PET Solved Paper-2009

  • question_answer
    The value of \[\underset{x\to 0}{\mathop{\lim }}\,\frac{(1-\cos 2x)}{{{x}^{2}}}\]is

    A)  doesn't exist       

    B)  infinite

    C)  0                  

    D)  2

    Correct Answer: D

    Solution :

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


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