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

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})

Plug in the value

h = 0

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

Simplify

= ln (a)

x \to 0 lim (\frac{8}{x ^{2}})

x \to \infty lim (x_{0})

x \to - 1 lim (\frac{14}{13} x - 1)

x \to x - lim (- \frac{1}{x + 1} - 1)

y \to 1 lim (y^{4} - 5 y^{3} + 2 y - 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)