What is the limit as x approaches 0 of ((2.7^x-1))/x ?

The limit as x approaches 0 of ((2.7^x-1))/x is 0.99325…

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 ((2.7^x-1))/x

x \to 0 lim (\frac{( 2. 7 ^{x} - 1 )}{x})

0.99325 \dots

Solution steps

x \to 0 lim (\frac{2. 7 ^{x} - 1}{x})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{0.99325 \dots \cdot 2. 7 ^{x}}{1})

Plug in the value

x = 0

= \frac{0.99325 \dots \cdot 2. 7 ^{0}}{1}

Simplify

= 0.99325 \dots

What is the limit as x approaches 0 of ((2.7^x-1))/x ?
The limit as x approaches 0 of ((2.7^x-1))/x is 0.99325…