What is the limit as x approaches 0 of (6^x-6^{-x})/x ?

The limit as x approaches 0 of (6^x-6^{-x})/x is 2ln(6)

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 (6^x-6^{-x})/x

x \to 0 lim (\frac{6 ^{x} - 6 ^{- x}}{x})

2 ln (6)

Decimal

3.58351 \dots

Solution steps

x \to 0 lim (\frac{6 ^{x} - 6 ^{- x}}{x})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{ln ( 6 ) \cdot 6 ^{x} + ln ( 6 ) \cdot 6 ^{- x}}{1})

Plug in the value

x = 0

= \frac{ln ( 6 ) \cdot 6 ^{0} + ln ( 6 ) \cdot 6 ^{- 0}}{1}

Simplify

\frac{ln ( 6 ) \cdot 6 ^{0} + ln ( 6 ) \cdot 6 ^{- 0}}{1} : 2 ln (6)

= 2 ln (6)

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

x \to \frac{π}{6} lim (2 sin (x))

x \to 2 lim (3 x^{3} + 7 x - 16)

x \to \infty lim (\frac{2}{3} x)

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

What is the limit as x approaches 0 of (6^x-6^{-x})/x ?
The limit as x approaches 0 of (6^x-6^{-x})/x is 2ln(6)