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

The limit as x approaches 1-of 1-e^{1/(x-1)} is 1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches 1-of 1-e^{1/(x-1)}

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

1

Solution steps

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

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

x \to 1 - lim (1) = 1

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

= 1 - 0

Simplify

= 1

What is the limit as x approaches 1-of 1-e^{1/(x-1)} ?
The limit as x approaches 1-of 1-e^{1/(x-1)} is 1