What is the limit as h approaches 0 of (6^h-1)/h ?

The limit as h approaches 0 of (6^h-1)/h is ln(6)

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limit as h approaches 0 of (6^h-1)/h

h \to 0 lim (\frac{6 ^{h} - 1}{h})

ln (6)

Decimal

1.79175 \dots

Solution steps

h \to 0 lim (\frac{6 ^{h} - 1}{h})

Apply L'Hopital's Rule

= h \to 0 lim (\frac{ln ( 6 ) \cdot 6 ^{h}}{1})

Plug in the value

h = 0

= \frac{ln ( 6 ) \cdot 6 ^{0}}{1}

Simplify

= ln (6)

What is the limit as h approaches 0 of (6^h-1)/h ?
The limit as h approaches 0 of (6^h-1)/h is ln(6)