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lim-x-1-1-ln-x-1-x-1-




Question Number 131962 by EDWIN88 last updated on 10/Feb/21
 lim_(x→1^+ ) ((1/(ln x)) − (1/(x−1)))=?
limx1+(1lnx1x1)=?
Answered by liberty last updated on 10/Feb/21
 let u=ln x ⇒x=e^u    lim_(u→0) ((1/u)−(1/(e^u −1)))   = lim_(u→0) (((e^u −1−u)/(u(e^u −1))))  = lim_(u→0) (((e^u −1)/(e^u −1+ue^u )))  = lim_(u→0) ((e^u /(e^u +e^u +ue^u )))=(1/2)
letu=lnxx=eulimu0(1u1eu1)=limu0(eu1uu(eu1))=limu0(eu1eu1+ueu)=limu0(eueu+eu+ueu)=12

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