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how do you take a limit of [ln(1+e^n)]/2n as n goes to infinity?

  • calculus -

    Take the limit of the ratio of the derivatives of numerator and denominator, with respect to n.

    That ratio is the limit of
    e^n/[2(1 + e^n)]

    which approaches 1/2 since 1 becomes negligible compared to e^n, as n goes to infinity.

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