What is the limit as x approaches 0 of (10^x-e^x)/x ?

The limit as x approaches 0 of (10^x-e^x)/x is ln(10)-1

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 (10^x-e^x)/x

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

ln (10) - 1

Decimal Notation

1.30258 \dots

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1 0 ^{x} ln ( 10 ) - e ^{x}}{1})

= x \to 0 lim (\frac{1 0 ^{x} ln ( 10 ) - e ^{x}}{1})

Plug in the value

x = 0

= \frac{1 0 ^{0} ln ( 10 ) - e ^{0}}{1}

Simplify

= ln (10) - 1

x \to - \infty lim (\frac{x}{3})

f (x) =, x

\frac{d}{d x} (15 - x^{2})

\int \frac{- 7 x - 7}{2 x ^{2} + 5 x - 3} d x

t \to 0 lim (\frac{( 5 e ^{t} - 5 )}{t})

What is the limit as x approaches 0 of (10^x-e^x)/x ?
The limit as x approaches 0 of (10^x-e^x)/x is ln(10)-1