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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        Let\[f(x)=\frac{1-\tan x}{4x-\pi },x\ne \frac{\pi }{4},x\in \left[ 0,\frac{\pi }{2} \right].F(x)\]is  continuous in\[\left[ 0,\frac{\pi }{2} \right],\]then\[\frac{dy}{dx}\]is

    A)  \[-\frac{1}{2}\]                                

    B)  \[\frac{1}{2}\]

    C)  \[1\]                                    

    D)  \[-1\]

    Correct Answer: A

    Solution :

                    \[\underset{x\to \frac{\pi }{4}}{\mathop{\lim }}\,f(x)=\underset{x\to \frac{\pi }{4}}{\mathop{\lim }}\,\frac{1-\tan x}{4x-\pi }\]                              \[\left( form\frac{0}{0} \right)\] \[=\underset{x\to \frac{\pi }{4}}{\mathop{\lim }}\,\frac{-{{\sec }^{2}}x}{4}=-\frac{1}{2}\]


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