limx→∞x(lnx)3=∞
One way to think of this problem is in terms of the relative growth rates between the numerator and denominator. I know that x grows asymptotically faster than (lnx)3 according to WolframAlpha. How can I prove this?
Answer
limx→∞x(lnx)3=(∞∞form, using L'Hospital rule)=limx→∞x3(lnx)2(∞∞form, using L'Hospital rule)=limx→∞x6(lnx)(∞∞form, using L'Hospital rule)=limx→∞x6=∞
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