2. Solved Papers
  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2004

  • question_answer
    Let\[f:R\to R\]be a differentiable function and \[f(1)=4.\]Then the value of\[\underset{x\to 1}{\mathop{\lim }}\,\int_{4}^{f(x)}{\frac{2t}{x-1}}dt,\]if \[f(1)=2\]is:

    A)  16                                         

    B)  8

    C)  4                            

    D)         2

    E)  1        

    Correct Answer: A

    Solution :

    \[\underset{x\to 1}{\mathop{\lim }}\,\frac{\int_{4}^{f(x)}{2t\,\,dt}}{x-1}\] \[=\underset{x\to 1}{\mathop{\lim }}\,\frac{2f(x).f(x)}{1}\] \[=2f(1).f(1)=2.4.2=16\]               


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