What is the limit as x approaches-infinity of (4x^6)/(x^3-8) ?

The limit as x approaches-infinity of (4x^6)/(x^3-8) is -infinity

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limit as x approaches-infinity of (4x^6)/(x^3-8)

x \to - \infty lim (\frac{4 x ^{6}}{x ^{3} - 8})

- \infty

Solution steps

x \to - \infty lim (\frac{4 x ^{6}}{x ^{3} - 8})

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

= 4 \cdot x \to - \infty lim (\frac{x ^{6}}{x ^{3} - 8})

Divide by highest denominator power:

\frac{x ^{3}}{1 - \frac{8}{x ^{3}}}

= 4 \cdot x \to - \infty lim (\frac{x ^{3}}{1 - \frac{8}{x ^{3}}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= 4 \cdot \frac{lim _{x \to - \infty} ( x ^{3} )}{lim _{x \to - \infty} ( 1 - \frac{8}{x ^{3}} )}

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

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

= 4 \cdot \frac{- \infty}{1}

Simplify

4 \cdot \frac{- \infty}{1} : - \infty

= - \infty

θ \to \frac{π}{3} lim (\frac{tan ( θ )}{sin ^{2} ( θ )})

\int \frac{x ^{2}}{( x + 1 ) ^{50}} d x

\frac{\partial}{\partial x} (2 x e^{- y})

\int (2 x - 1) ln (17 x) d x

\frac{2}{x}, 4 x, \frac{4}{x}

What is the limit as x approaches-infinity of (4x^6)/(x^3-8) ?
The limit as x approaches-infinity of (4x^6)/(x^3-8) is -infinity