What is the limit as x approaches 0+of 1/(1-e^x)-1/x ?

The limit as x approaches 0+of 1/(1-e^x)-1/x is -infinity

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 0+of 1/(1-e^x)-1/x

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

- \infty

Solution steps

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

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

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

= - \infty - \infty

Apply Infinity Property:

- \infty - \infty = - \infty

= - \infty

\frac{d}{d x} (\frac{1}{x ^{2}} + \frac{1}{x})

\int 6 sin^{2} (x) cos^{2} (x) d x

n = 1 \sum \infty \frac{3}{2 n}

\frac{\partial}{\partial x} (e^{x + 2 y})

(ln (x^{2} + 8 x + 21))^{^{'}}

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