What is the limit as x approaches 0-of (1-e^{-3x})/x ?

The limit as x approaches 0-of (1-e^{-3x})/x is 3

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-e^{-3x})/x

x \to 0 - lim (\frac{1 - e ^{- 3 x}}{x})

3

Solution steps

x \to 0 - lim (\frac{1 - e ^{- 3 x}}{x})

Apply L'Hopital's Rule

: x \to 0 - lim (\frac{3 e ^{- 3 x}}{1})

= x \to 0 - lim (\frac{3 e ^{- 3 x}}{1})

Plug in the value

x = 0

= \frac{3 e ^{- 3 \cdot 0}}{1}

Simplify

= 3

\frac{d}{d x} (\frac{e ^{x}}{7 x ^{2} + 8})

\int_{0}^{5} ∣ x - 3 ∣ d x

\int x 1 3^{x} d x

\int y^{2} sinh (5 y) d y

\int_{0}^{1} \int_{0}^{x} \frac{4 - 2 y}{( 1 + x ) ^{2}} d y d x

What is the limit as x approaches 0-of (1-e^{-3x})/x ?
The limit as x approaches 0-of (1-e^{-3x})/x is 3