What is the limit as x approaches infinity of (\sqrt[3]{8x^9+x^6+2})/(4x^3+x^2-1) ?

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limit as x approaches infinity of (\sqrt[3]{8x^9+x^6+2})/(4x^3+x^2-1)

\frac{1}{2}

Decimal

0.5

Solution steps

Divide by highest denominator power:

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

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

= \frac{2}{4}

Cancel the common factor:

2

= \frac{1}{2}

What is the limit as x approaches infinity of (\sqrt[3]{8x^9+x^6+2})/(4x^3+x^2-1) ?
The limit as x approaches infinity of (\sqrt[3]{8x^9+x^6+2})/(4x^3+x^2-1) is 1/2