What is the limit as x approaches+0 of (e^{9x}-1)/x ?

The limit as x approaches+0 of (e^{9x}-1)/x is 9

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 (e^{9x}-1)/x

x \to + 0 lim (\frac{e ^{9 x} - 1}{x})

9

Solution steps

x \to 0 lim (\frac{e ^{9 x} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{9 e ^{9 x}}{1})

= x \to 0 lim (\frac{9 e ^{9 x}}{1})

Plug in the value

x = 0

= \frac{9 e ^{9 \cdot 0}}{1}

Simplify

= 9

\int_{0}^{5} 2 π x (5 x - x^{2}) d x

\int_{3}^{4} - \frac{1}{( x - 3 ) ^{3}} d x

\frac{d}{d x} (e^{x} - sin (x))

x, - 1, 1

y^{^{'}} + 6 x y = x^{4} e^{\frac{- 6 x ^{2}}{2}}

What is the limit as x approaches+0 of (e^{9x}-1)/x ?
The limit as x approaches+0 of (e^{9x}-1)/x is 9