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Question Number 62067 by naka3546 last updated on 15/Jun/19

lim_(x → −1)   ((x^3  + 2x^2  − 1)/((x + 1)^2 ))  =  ?

limx1x3+2x21(x+1)2=?

Commented by gunawan last updated on 15/Jun/19

lim_(x→−1)  ((3x^2 +4x)/(2x+2))  lim_(x→−1)  ((6x+4)/2)=3x+2=−1

limx13x2+4x2x+2limx16x+42=3x+2=1

Commented by Tony Lin last updated on 15/Jun/19

lim_(x→−1) ((x^3 +2x^2 −1)/((x+1)^2 ))  =lim_(x→−1) (((x+1)(x^2 +x−1))/((x+1)^2 ))  =lim_(x→−1) ((x^2 +x−1)/(x+1))(not(0/0))  ⇒the value does not exist

limx1x3+2x21(x+1)2=limx1(x+1)(x2+x1)(x+1)2=limx1x2+x1x+1(not00)thevaluedoesnotexist

Commented by Tony Lin last updated on 15/Jun/19

3×(−1)^2 +4×(−1)=−1≠0

3×(1)2+4×(1)=10

Answered by MIR ZAKIR last updated on 15/Jun/19

lim  x−φ

limxϕ

Answered by MJS last updated on 15/Jun/19

((x^3 +2x^2 −1)/((x+1)^2 ))=((x^2 +x−1)/(x+1))=x−(1/(x+1))=  let x=t−1  =t−1−(1/t)  lim_(t→0)  (1/t) doesn′t exist ⇒ lim_(t→0)  t−1−(1/t) doesn′t exist ⇒  ⇒ lim_(x→−1) ((x^3 +2x^2 −1)/((x+1)^2 )) doesn′t exist

x3+2x21(x+1)2=x2+x1x+1=x1x+1=letx=t1=t11tlimt01tdoesntexistlimt0t11tdoesntexistlimx1x3+2x21(x+1)2doesntexist

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