Question

Limite de x tendendo a -1 x^3+1/x^2-1

Answer 1

$Boa\; noite!\\ \\ \lim_{x \to (- 1)} \frac{x^3\;+\;1}{x^2\;-\;1} \\ \\ \lim_{x \to (-1)} \frac{(-1)^3\;+\;1}{(-1)^2\;-\;1} \\ \\ \lim_{x \to (-1)} \frac{-1\;+\;1}{1\;-\;1} \\ \\ \lim_{x \to (-1)} = \frac{0}{0} \ \textless \ ------ indeterminacao\\ \\ Aplicando L'Hospital\\ \\ fazemos\;a\;primeira \;derivada..\\ \\ \frac{3x^2}{2x} \\ \\ \lim_{x \to (-1)} \frac{3.(-1)^2}{2.(-1)} \\ \\ \lim_{x \to(-1)} \frac{3}{-2} \\ \\ \lim_{x \to (-1)} = \frac{-3}{2} \\ \\ Bons \;estudos!$

Answer 2

Lim (x³+1)/(x²-1)

x-->-1

***(x+1)³=x³+1+3x+3x²

***(x+1)³=x³+1+3x(x+1)

***x³+1 =(x+1)*[(x+1)²-3x

**x³+1= (x+1)(x²+1-x)

### (x²-1) =(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