Friday, 27 December 2013

calculus - Prove limxtoinftyfracx(lnx)3=infty



limxx(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



limxx(lnx)3=(form, using L'Hospital rule)=limxx3(lnx)2(form, using L'Hospital rule)=limxx6(lnx)(form, using L'Hospital rule)=limxx6=


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