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  3. RAJASTHAN ­ PET

RAJASTHAN ­ PET Rajasthan PET Solved Paper-2001

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{x}{{{\tan }^{-1}}2x}\]is equal to

    A)  2

    B)  \[\frac{1}{2}\]

    C)  0                

    D)  None of these

    Correct Answer: B

    Solution :

     \[\underset{x\to 0}{\mathop{\lim }}\,\frac{x}{{{\tan }^{-1}}2x}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{1}{2.\frac{1}{1+4{{x}^{2}}}}\] (by L-Hospital rule) \[=\frac{1}{2}\]


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