I need step by step help for this please and a detailed explanation... Using L\'

Question

I need step by step help for this please and a detailed explanation... Using L'Hopital Rule limit x--> infinity (lnx)^2/(x) This is the answer, but I need EXPLANATIONS for each step please!! lim (x->inf) (ln x)^2 / x = lim (x->inf) [2(ln x)(1/x)] / x (By l'hopital's rule) = lim (x->inf) [2(ln x)] / x^2 = lim (x->inf) (2/x) / 2x (By L'hopsital rule) = lim (x->inf) 1 / x^2 = 0

Explanation / Answer

limit x--> infinity (lnx)^2/(x) = infinity/infinity = indeterminate form so apply L' Hopital's Rule = lim (x->inf) [2(ln x)(1/x)] / 1 (by differentiating both numerator and denominator) = infinity/infinity = indeterminate form so apply L' Hopital's Rule = lim (x->inf) 2(1/x)/1 = 2/infinity = 0

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