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Question Number 27723 by NECx last updated on 13/Jan/18

lim_(x→1) ((x^3 −1)/((x−1)^2 ))

limx→1x3−1(x−1)2

Answered by prakash jain last updated on 13/Jan/18

((x^3 −1)/((x−1)^2 ))=((x^2 +x+1)/(x−1)) lim_(x→1^+ ) ((x^2 +x+1)/(x−1))=lim_(h→0^+ ) =(((1+h)^2 +(1+h)+1)/h)=+∞ lim_(x→1^− ) ((x^2 +x+1)/(x−1))=lim_(h→0^+ ) =(((1−h)^2 +(1−h)+1)/(−h))=−∞ limit does not exist

x3−1(x−1)2=x2+x+1x−1limx→1+x2+x+1x−1=limh→0+=(1+h)2+(1+h)+1h=+∞limx→1−x2+x+1x−1=limh→0+=(1−h)2+(1−h)+1−h=−∞limitdoesnotexist

Commented by NECx last updated on 13/Jan/18

thanks

thanks

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