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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2009

  • question_answer
        The interval of increase of the function\[f(x)=x-{{e}^{x}}+\tan (2\pi /7)\]is

    A)  \[(0,\infty )\]                                   

    B)  \[(-\infty ,0)\]

    C)  \[(1,\infty )\]                                   

    D)  \[(-\infty ,-1)\]

    Correct Answer: B

    Solution :

                    We have, \[f(x)=x-{{e}^{x}}+\tan \left( \frac{2\pi }{7} \right)\] \[\Rightarrow \]               \[f(x)=1-{{e}^{x}}\] For\[f(x)\]to be increasing, we must have                 \[f(x)>0\Rightarrow 1-{{e}^{x}}>0\Rightarrow {{e}^{x}}<1\] \[\Rightarrow \] \[x<0\]\[\Rightarrow \] \[x\in (-\infty ,0)\]


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