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calculus

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Using L'Hôpital's rule, evaluate lim of xe^(-x) as x approaches infinity

  • calculus -

    X=Lim xe^(-x)
    x->∞
    =Lim x/e^x
    x->∞

    L'hôpital's rule is applicable if direct evaluation results in an indeterminate form, which is the case here.
    To apply the rule, differentiate both numerator and denominator to give
    X=Lim 1/e^x
    x->∞
    =0

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