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})

= 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)

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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)