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

The limit as x approaches-infinity of (2x)/(\sqrt[3]{x^6-1)} is 0

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

0

Solution steps

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

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 (\frac{1}{x}) = 0

= 2 \cdot \frac{0}{1}

Simplify

2 \cdot \frac{0}{1} : 0

= 0

x \to 0 lim (sin (\frac{3 x}{x}))

x \to 1 lim (\frac{cos ( \frac{π}{2} x )}{x - 1})

x \to 0 lim ((1 + \frac{x}{4})^{\frac{1}{x}})

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

What is the limit as x approaches-infinity of (2x)/(\sqrt[3]{x^6-1)} ?
The limit as x approaches-infinity of (2x)/(\sqrt[3]{x^6-1)} is 0