Asked by Anonymous
Posted question rewritten
lim
x-> -1
108(x^2+2x)(x+1)^3
____________________
(x^3+1)^3 (x-1)
lim
x-> -1
108(x^2+2x)(x+1)^3
____________________
(x^3+1)^3 (x-1)
Answers
Answered by
Reiny
look at the bottom, this factors to
[(x+1)(x^2 - x + 1)]^3
or (x+1)^3(x^2 - x + 1)^3
so you have
lim(108(x^2 + 2x)/[(x^2 - x + 1)^3(x-1) as x ---> -1
= 108(1-2)/[(1 + 1 + 1)^3(-2)]
= -108/-54
= 2
[(x+1)(x^2 - x + 1)]^3
or (x+1)^3(x^2 - x + 1)^3
so you have
lim(108(x^2 + 2x)/[(x^2 - x + 1)^3(x-1) as x ---> -1
= 108(1-2)/[(1 + 1 + 1)^3(-2)]
= -108/-54
= 2
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