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lim-x-1-x-x-1-x-2-1-

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Question Number 106313 by bemath last updated on 04/Aug/20
lim_(x→1) ((x∣x−1∣)/(x^2 −1))
limx→1x∣x−1∣x2−1
Answered by Dwaipayan Shikari last updated on 04/Aug/20
first case lim_(x→1^+ ) ((x(x−1))/(x^2 −1))=(x/(x+1))=(1/2) second case lim_(x→1) −((x(x−1))/(x^2 −1))=−(1/2) L.H.S≠R.H.S(limit doesn′t exist)
firstcaselimx→1+x(x−1)x2−1=xx+1=12secondcaselimx→1−x(x−1)x2−1=−12L.H.S≠R.H.S(limitdoesn′texist)

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