What is the limit as h approaches 0 of (10^h-1)/h ?

The limit as h approaches 0 of (10^h-1)/h is ln(10)

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limit as h approaches 0 of (10^h-1)/h

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

ln (10)

Decimal

2.30258 \dots

Solution steps

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

Apply L'Hopital's Rule

: h \to 0 lim (\frac{ln ( 10 ) \cdot 1 0 ^{h}}{1})

= h \to 0 lim (\frac{ln ( 10 ) \cdot 1 0 ^{h}}{1})

Plug in the value

h = 0

= \frac{ln ( 10 ) \cdot 1 0 ^{0}}{1}

Simplify

= ln (10)

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What is the limit as h approaches 0 of (10^h-1)/h ?
The limit as h approaches 0 of (10^h-1)/h is ln(10)