What is the limit as x approaches infinity of \sqrt[3]{27+6/x}-3 ?

The limit as x approaches infinity of \sqrt[3]{27+6/x}-3 is 0

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limit as x approaches infinity of \sqrt[3]{27+6/x}-3

x \to \infty lim (3 27 + \frac{6}{x} - 3)

0

Solution steps

x \to \infty lim (3 27 + \frac{6}{x} - 3)

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to \infty lim (3 27 + \frac{6}{x}) - x \to \infty lim (3)

x \to \infty lim (3 27 + \frac{6}{x}) = 3

x \to \infty lim (3) = 3

= 3 - 3

Simplify

= 0

x \to \infty lim (\frac{cosh ( 2 x )}{e ^{2 x}})

x \to 0 lim (\frac{cos ( 3 x ) - cos ( 4 x )}{x ^{2}})

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

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

b \to 1 - lim (- ln (1 - b))

What is the limit as x approaches infinity of \sqrt[3]{27+6/x}-3 ?
The limit as x approaches infinity of \sqrt[3]{27+6/x}-3 is 0