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

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

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

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

ln (2)

Decimal

0.69314 \dots

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

Simplify

= ln (2)

\int \frac{1}{y ^{2} - y ^{3}} d y

\int x^{3} (\frac{2 x ^{2} + 1}{x}) d x

d er i v a t i v e \frac{x}{x + 3}

\int_{0}^{2} 5^{- x} d x

x y^{^{'}} + 15 y = 0

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