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J & K CET Engineering J and K - CET Engineering Solved Paper-2014

  • question_answer
    If \[g(x)=({{x}^{2}}+2x+3)\,f(x),\,\,f(0)=5\] and \[{{\lim }_{x\to 0}}\,\frac{f(x)-5)}{x}=4,\]then \[f'(0)\] equal to

    A)  \[22\]    

    B)  \[18\]     

    C)  \[20\]    

    D)  \[25\]

    E)  None of these

    Correct Answer: E

    Solution :

    Given,  \[g(x)=({{x}^{2}}+2x+3)f(x),f(0)=5\] and \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\left[ \frac{f(x)-5}{x} \right]=4\] \[f'(0)=\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{f(0+x)-f(0)}{x-0}\] \[=\underset{x-0}{\mathop{\lim }}\,\frac{f(x)-5}{x}\] \[\Rightarrow \] \[f'(0)=4\]


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