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Prove-lim-x-1-1-x-ln-1-x-0-

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Question Number 26591 by prakash jain last updated on 27/Dec/17
Prove lim_(x→−1) (1+x)ln (1+x)=0
Provelimx→−1(1+x)ln(1+x)=0
Commented by abdo imad last updated on 27/Dec/17
let put 1+x=u ⇒ lim_(x−>−1^+ ) (1+x)ln(1+x) =lim_(u−>0^+ ) ulnu =0
letput1+x=u⇒limx−>−1+(1+x)ln(1+x)=limu−>0+ulnu=0
Answered by ajfour last updated on 27/Dec/17
L=lim_(x→−1) ((ln (1+x))/(((1/(1+x))))) =lim_(x→−1) [−(((1+x)^2 )/(1+x))]=−lim_(x→−1) (1+x)=0 .
L=limx→−1ln(1+x)(11+x)=limx→−1[−(1+x)21+x]=−limx→−1(1+x)=0.

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