What is the limit as x approaches infinity of (\sqrt[3]{x}+5x+3)/(-2x+x^{2/3)+7} ?

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limit as x approaches infinity of (\sqrt[3]{x}+5x+3)/(-2x+x^{2/3)+7}

- \frac{5}{2}

Decimal Notation

- 2.5

Solution steps

Divide by highest denominator power:

\frac{\frac{1}{x ^{\frac{2}{3}}} + 5 + \frac{3}{x}}{- 2 + \frac{1}{x ^{\frac{1}{3}}} + \frac{7}{x}}

= x \to \infty lim (\frac{\frac{1}{x ^{\frac{2}{3}}} + 5 + \frac{3}{x}}{- 2 + \frac{1}{x ^{\frac{1}{3}}} + \frac{7}{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

= \frac{lim _{x \to \infty} ( \frac{1}{x ^{\frac{2}{3}}} + 5 + \frac{3}{x} )}{lim _{x \to \infty} ( - 2 + \frac{1}{x ^{\frac{1}{3}}} + \frac{7}{x} )}

x \to \infty lim (\frac{1}{x ^{\frac{2}{3}}} + 5 + \frac{3}{x}) = 5

x \to \infty lim (- 2 + \frac{1}{x ^{\frac{1}{3}}} + \frac{7}{x}) = - 2

= \frac{5}{- 2}

Simplify

= - \frac{5}{2}

f (x) = 2 x^{3} - x^{2} + 2, (1, 3)

x \to - 1 + lim (f (x))

\int 5 x cos (6 x) d x

x \to 0 lim ((1 + \frac{1}{x})^{3 x})

x \frac{d y}{d x} - 4 y = 6 x^{4} e^{x}

What is the limit as x approaches infinity of (\sqrt[3]{x}+5x+3)/(-2x+x^{2/3)+7} ?
The limit as x approaches infinity of (\sqrt[3]{x}+5x+3)/(-2x+x^{2/3)+7} is -5/2