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

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

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

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

- \infty

Solution steps

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

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 1 + \frac{2}{x}) - x \to \infty lim (x)

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

x \to \infty lim (x) = \infty

= 1 - \infty

Apply Infinity Property:

c - \infty = - \infty

= - \infty

\frac{d}{d x} (- \frac{8}{x ^{3}} + \frac{2}{x ^{2}})

\int \frac{e ^{a r c t a n (x)} + 1}{1 + x ^{2}} d x

x \to - 1 - lim (\frac{x}{∣ x - 1 ∣})

\int 4 sin (x + \frac{π}{4}) cos (x - \frac{π}{4}) d x

\frac{\partial}{\partial x} (\frac{x ( v - b )}{r ( x , v )})

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