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)

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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)

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

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

x \to 0 lim (\frac{1}{6 x})

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

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

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)