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

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

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limit as h approaches 0 of (2^h-1)/h

h \to 0 lim (\frac{2 ^{h} - 1}{h})

ln (2)

Decimal Notation

0.69314 \dots

Solution steps

h \to 0 lim (\frac{2 ^{h} - 1}{h})

Apply L'Hopital's Rule

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

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

Plug in the value

h = 0

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

Simplify

= ln (2)

\frac{d}{d x} (x^{6})

x \to 4 lim (+ (2 x - 4))

v \frac{d v}{d y} + v^{2} = 2 e^{- y}

\frac{d}{d x} (\frac{( x ^{2} - 2 )}{x})

\frac{d}{d x} ((1 - 3 x^{2})^{\frac{1}{s i n ^{2} ( x )}})

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