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JEE Main & Advanced Mathematics Differentiation Question Bank Self Evaluation Test - Limits and Derivatives

  • question_answer
    If \[x>0\] and \[g\] is  a bounded function, then \[\underset{n\,\to \,\infty }{\mathop{\lim }}\,\frac{f(x){{e}^{nx}}+g(x)}{{{e}^{nx}}+1}\] is

    A) 0

    B) \[f(x)\]

    C) \[g(x)\]

    D) None of these

    Correct Answer: B

    Solution :

    [b] Given that, x > 0 and g(x) is bounded function. \[Limit=\underset{n\to \infty }{\mathop{\lim }}\,\frac{f(x){{e}^{nx}}+g(x)}{{{e}^{nx}}+1}\] \[=\underset{n\to \infty }{\mathop{\lim }}\,\frac{f(x)}{1+\left( \frac{1}{{{e}^{nx}}} \right)}+\frac{g(x)}{{{e}^{nx}}+1}=\frac{f(x)}{1+0}+\frac{finite}{\infty }\] \[=f(x)\]


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