What is the limit as h approaches 0 of (4^h-1)/h ?

The limit as h approaches 0 of (4^h-1)/h is 2ln(2)

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limit as h approaches 0 of (4^h-1)/h

h \to 0 lim (\frac{4 ^{h} - 1}{h})

2 ln (2)

Decimal

1.38629 \dots

Solution steps

h \to 0 lim (\frac{4 ^{h} - 1}{h})

Apply L'Hopital's Rule

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

Plug in the value

h = 0

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

Simplify

= 2 ln (2)

What is the limit as h approaches 0 of (4^h-1)/h ?
The limit as h approaches 0 of (4^h-1)/h is 2ln(2)