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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

e

Decimal

2.71828 \dots

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 1

= \frac{e ^{1}}{1}

Simplify

= e

5 x + 4

(arctan (3 x))^{^{'}}

y = (arctan (5 x))^{2}

y = (8 x - x^{2})^{3}

\int_{0}^{\frac{π}{6}} x sin (2 x) d x

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