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

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

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limit as h approaches 0 of (3^h-1)/h

h \to 0 lim (\frac{3 ^{h} - 1}{h})

ln (3)

Decimal

1.09861 \dots

Solution steps

h \to 0 lim (\frac{3 ^{h} - 1}{h})

Apply L'Hopital's Rule

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

Plug in the value

h = 0

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

Simplify

= ln (3)

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