What is the limit as h approaches 0 of ((8^h-1))/h ?

The limit as h approaches 0 of ((8^h-1))/h is 3ln(2)

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limit as h approaches 0 of ((8^h-1))/h

h \to 0 lim (\frac{( 8 ^{h} - 1 )}{h})

3 ln (2)

Decimal

2.07944 \dots

Solution steps

h \to 0 lim (\frac{8 ^{h} - 1}{h})

Apply L'Hopital's Rule

= h \to 0 lim (\frac{3 ln ( 2 ) \cdot 8 ^{h}}{1})

Plug in the value

h = 0

= \frac{3 ln ( 2 ) \cdot 8 ^{0}}{1}

Simplify

= 3 ln (2)

d er i v a t i v e t^{2} - 8 t + 19

\frac{\partial}{\partial x} (\frac{ln ^{^{'}} ( x ^{2} + 5 )}{y ^{2}})

\frac{\partial}{\partial z} (x y arcsin (yz))

\frac{d}{d x} (3 + \frac{1}{2} cosh (2 x))

t an g e n t f (x) = x^{2} - 9 x + 17, at x = 4

What is the limit as h approaches 0 of ((8^h-1))/h ?
The limit as h approaches 0 of ((8^h-1))/h is 3ln(2)