What is the limit as x approaches infinity of (7x-1)/(\sqrt[3]{5x^3+4x-1)} ?

The limit as x approaches infinity of (7x-1)/(\sqrt[3]{5x^3+4x-1)} is 7/(\sqrt[3]{5)}

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limit as x approaches infinity of (7x-1)/(\sqrt[3]{5x^3+4x-1)}

Decimal

4.09362 \dots

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 (7 - \frac{1}{x}) = 7

What is the limit as x approaches infinity of (7x-1)/(\sqrt[3]{5x^3+4x-1)} ?
The limit as x approaches infinity of (7x-1)/(\sqrt[3]{5x^3+4x-1)} is 7/(\sqrt[3]{5)}