What is the limit as x approaches-2-of (1-x)/(x^3+8) ?

The limit as x approaches-2-of (1-x)/(x^3+8) is -infinity

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limit as x approaches-2-of (1-x)/(x^3+8)

x \to - 2 - lim (\frac{1 - x}{x ^{3} + 8})

- \infty

Solution steps

x \to - 2 - lim (\frac{1 - x}{x ^{3} + 8})

\frac{1 - x}{x ^{3} + 8} = (1 - x) \frac{1}{x ^{3} + 8}

= x \to - 2 - lim ((1 - x) \frac{1}{x ^{3} + 8})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to - 2 - lim (1 - x) \cdot x \to - 2 - lim (\frac{1}{x ^{3} + 8})

x \to - 2 - lim (1 - x) = 3

x \to - 2 - lim (\frac{1}{x ^{3} + 8}) = - \infty

= 3 (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

\frac{d}{d x} ((1 + i)^{x})

\frac{\partial}{\partial x} ((4 x + 8) ln (6 x y))

\frac{d}{d x} (4 e^{- 3 x})

\frac{d}{d x} (- cos (2 x) - 2 sin (2 x) (1 - x))

x \frac{d y}{d x} + 2 y = x^{2}

What is the limit as x approaches-2-of (1-x)/(x^3+8) ?
The limit as x approaches-2-of (1-x)/(x^3+8) is -infinity