What is the limit as x approaches infinity of \sqrt[3]{(5-8x)/(x+3)} ?

The limit as x approaches infinity of \sqrt[3]{(5-8x)/(x+3)} is 2\sqrt[3]{-1}

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limit as x approaches infinity of \sqrt[3]{(5-8x)/(x+3)}

Solution steps

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

Divide by highest denominator power:

\frac{\frac{5}{x} - 8}{1 + \frac{3}{x}}

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{5}{x} - 8) = - 8

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

Simplify

\int \frac{x + 4}{x ^{2} + 4} d x

(x + 2)^{3}, 2 x^{2} - 8 x + 8, 0

x \to 1 lim (x + 4 - 12)

f (x) = x + 2, at x = 1

f (x) = lo g_{4} (3 x^{2} + 1)

What is the limit as x approaches infinity of \sqrt[3]{(5-8x)/(x+3)} ?
The limit as x approaches infinity of \sqrt[3]{(5-8x)/(x+3)} is 2\sqrt[3]{-1}