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Calculus

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What is the limit of the following equation?
Limit as x approaches infinity of ((e^x) - ln(x)) / (x^3)

  • Calculus -

    Since both numerator and denominator approach infinity as x→∞, we can apply l'Hôpital's rule:
    (ex-(1/x))/3x²
    Rewrite as a sum:
    ex/3x² -(1/x)/3x²
    the second term goes to zero as x→∞.
    Apply the rule again to the first term:
    ex/6x;
    Apply the rule one last time:
    ex/6; which goes to ∞ as x→&infin.
    So the limit is ∞.

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