What is the limit as x approaches 0-of 1/(|x|)-1/x ?

The limit as x approaches 0-of 1/(|x|)-1/x 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 0-of 1/(|x|)-1/x

x \to 0 - lim (\frac{1}{∣ x ∣} - \frac{1}{x})

\infty

Solution steps

x \to 0 - lim (\frac{1}{∣ x ∣} - \frac{1}{x})

x

is negative when

x \to 0 -

. Therefore

∣ x ∣ = - x

= x \to 0 - lim (\frac{1}{- x} - \frac{1}{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 0 - lim (\frac{1}{- x}) - x \to 0 - lim (\frac{1}{x})

x \to 0 - lim (\frac{1}{- x}) = \infty

x \to 0 - lim (\frac{1}{x}) = - \infty

= \infty - (- \infty)

Apply Infinity Property:

\infty + \infty = \infty

= \infty

What is the limit as x approaches 0-of 1/(|x|)-1/x ?
The limit as x approaches 0-of 1/(|x|)-1/x is infinity