What is the limit as x approaches infinity of (x^3+x)/(3-x) ?

The limit as x approaches infinity of (x^3+x)/(3-x) is -infinity

limit as x approaches infinity of (x^3+x)/(3-x)

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

- \infty

Solution steps

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

Divide by highest denominator power:

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

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

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

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

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

= \frac{\infty}{- 1}

Apply Infinity Property:

\frac{\infty}{- c} = - \infty

= - \infty

x \to 6 lim (x - 1)

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

x \to 0 - lim (x^{2} e^{- \frac{1}{x ^{2}}})

x \to 0 lim (\frac{3}{3 x + 4 + 4})

x \to 1 lim (x ln ∣ x - 1 ∣)

What is the limit as x approaches infinity of (x^3+x)/(3-x) ?
The limit as x approaches infinity of (x^3+x)/(3-x) is -infinity