What is the limit as h approaches 0 of (a^h-1)/h ?

The limit as h approaches 0 of (a^h-1)/h is ln(a)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as h approaches 0 of (a^h-1)/h

h \to 0 lim (\frac{a ^{h} - 1}{h})

ln (a)

Solution steps

h \to 0 lim (\frac{a ^{h} - 1}{h})

Apply L'Hopital's Rule

: h \to 0 lim (\frac{a ^{h} ln ( a )}{1})

= h \to 0 lim (\frac{a ^{h} ln ( a )}{1})

Plug in the value

h = 0

= \frac{a ^{0} ln ( a )}{1}

Simplify

= ln (a)

y^{^{'}} = \frac{2 y}{tan ( x )}

\int_{x}^{10} t^{3} d t

\frac{d}{d x} (8 - 3 x)

x \to \infty lim (x^{9})

\frac{2 x}{( 1 + x ^{2} ) ^{2}}

What is the limit as h approaches 0 of (a^h-1)/h ?
The limit as h approaches 0 of (a^h-1)/h is ln(a)