Question

Calcule e justifique:
$\lim_{x \to \ -1} \frac{x^{3}+1}{x^{2}-1}$

Answer 1

(x+1)³=x³+3x²+3x+1
(x+1)³=x³+1+3x*(x+1)
x³+1 =(x+1)³-3x*(x+1)
x³+1=(x+1)*[(x+1)²-3x]
x³+1=(x+1)*[x²+2x+1-3x]
x³+1=(x+1)*(x²+1-x)

x²-1=(x+1)*(x-1)

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Lim (x+1)*(x²+1-x)/(x+1)*(x-1)
x-->-1 

Lim (x+1)*(x²+1-x)/(x+1)*(x-1)
x-->-1 


Lim (x²+1-x)/(x-1)  =(1+1+1)/(-2) =-3/2
x-->-1