What is the limit as x approaches-2 of (2x^3+9x^2+12x+4)/(-x^3-2x^2+4x+8) ?

The limit as x approaches-2 of (2x^3+9x^2+12x+4)/(-x^3-2x^2+4x+8) is -3/4

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limit as x approaches-2 of (2x^3+9x^2+12x+4)/(-x^3-2x^2+4x+8)

x \to - 2 lim (\frac{2 x ^{3} + 9 x ^{2} + 12 x + 4}{- x ^{3} - 2 x ^{2} + 4 x + 8})

- \frac{3}{4}

Decimal Notation

- 0.75

Solution steps

x \to - 2 lim (\frac{2 x ^{3} + 9 x ^{2} + 12 x + 4}{- x ^{3} - 2 x ^{2} + 4 x + 8})

Simplify

\frac{2 x ^{3} + 9 x ^{2} + 12 x + 4}{- x ^{3} - 2 x ^{2} + 4 x + 8} : - \frac{2 x + 1}{x - 2}

= x \to - 2 lim (- \frac{2 x + 1}{x - 2})

Plug in the value

x = - 2

= - \frac{2 ( - 2 ) + 1}{- 2 - 2}

Simplify

- \frac{2 ( - 2 ) + 1}{- 2 - 2} : - \frac{3}{4}

= - \frac{3}{4}

\int - x^{\frac{3}{2}} d x

\int_{- 1}^{1} (x^{3} - x) d x

\int_{0}^{c} 9 e^{3 x} d x

\frac{\partial}{\partial x} (3 sin (2 x y))

x \to \infty lim (e^{8 x})

What is the limit as x approaches-2 of (2x^3+9x^2+12x+4)/(-x^3-2x^2+4x+8) ?
The limit as x approaches-2 of (2x^3+9x^2+12x+4)/(-x^3-2x^2+4x+8) is -3/4