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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2010

  • question_answer
        If\[f(x)={{e}^{x}}g(x),g(0)=2,g(0)=1,\]then\[f(0)\]is equal to

    A)  1                                            

    B)  3

    C)  2                                            

    D)  0

    Correct Answer: B

    Solution :

                    \[f(x)={{e}^{x}}g(x)\] On differentiating with respect to\[x,\]we get \[f(x)={{e}^{x}}g(x)+{{e}^{x}}g(x)\] At\[x=0\]                 \[f(0)={{e}^{0}}g(0)+{{e}^{0}}g(0)\] \[\Rightarrow \]               \[f(0)=g(0)+g(0)\]                                 \[=1+2\] \[\Rightarrow \]               \[f(0)=3\]


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