What is the limit as x approaches-infinity of ((x^2-5x))/(x-2) ?

The limit as x approaches-infinity of ((x^2-5x))/(x-2) is -infinity

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches-infinity of ((x^2-5x))/(x-2)

x \to - \infty lim (\frac{( x ^{2} - 5 x )}{x - 2})

- \infty

Solution steps

x \to - \infty lim (\frac{x ^{2} - 5 x}{x - 2})

Divide by highest denominator power:

\frac{x - 5}{1 - \frac{2}{x}}

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

x \to - \infty lim (x - 5) = - \infty

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

= \frac{- \infty}{1}

Apply Infinity Property:

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

= - \infty

What is the limit as x approaches-infinity of ((x^2-5x))/(x-2) ?
The limit as x approaches-infinity of ((x^2-5x))/(x-2) is -infinity