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April 1, 2015

Posted by **ELIZABETH** on Thursday, May 31, 2012 at 2:01pm.

Limit as x approaches infinity of ((e^x) - ln(x)) / (x^3)

- Calculus -
**MathMate**, Thursday, May 31, 2012 at 3:54pmSince both numerator and denominator approach infinity as x→∞, we can apply l'Hôpital's rule:

(e^{x}-(1/x))/3x²

Rewrite as a sum:

e^{x}/3x² -(1/x)/3x²

the second term goes to zero as x→∞.

Apply the rule again to the first term:

e^{x}/6x;

Apply the rule one last time:

e^{x}/6; which goes to ∞ as x→&infin.

So the limit is ∞.

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