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

The limit as x approaches-4-of (-4x^3)/(4+x) is infinity

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limit as x approaches-4-of (-4x^3)/(4+x)

x \to - 4 - lim (\frac{- 4 x ^{3}}{4 + x})

\infty

Solution steps

x \to - 4 - lim (\frac{- 4 x ^{3}}{4 + x})

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

= - 4 \cdot x \to - 4 - lim (\frac{x ^{3}}{4 + x})

\frac{x ^{3}}{4 + x} = x^{3} \frac{1}{4 + x}

= - 4 \cdot x \to - 4 - lim (x^{3} \frac{1}{4 + x})

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

= - 4 \cdot x \to - 4 - lim (x^{3}) \cdot x \to - 4 - lim (\frac{1}{4 + x})

x \to - 4 - lim (x^{3}) = - 64

x \to - 4 - lim (\frac{1}{4 + x}) = - \infty

= - 4 (- 64) (- \infty)

Apply Infinity Property:

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

= \infty

x \to a + lim (x^{n})

\int \frac{x ^{6} + 4 x ^{3} + 4}{x ^{3} - 4 x ^{2}} d x

\frac{d}{d x} (cos (x) + x^{5})

\frac{d y}{d x} + 5 x y = 4 x

\int \frac{x ^{2} - 16}{x} d x

What is the limit as x approaches-4-of (-4x^3)/(4+x) ?
The limit as x approaches-4-of (-4x^3)/(4+x) is infinity