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

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

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

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

- ln (2)

Decimal

- 0.69314 \dots

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

= - ln (2)

f (x) = sec (2 x)

\int e^{x + e^{x}} d x

\frac{1}{s ^{2}} - \frac{48}{s ^{5}}

\int \frac{1}{x x ^{2} - 2} d x

f (x) = 8 x - 3 x^{2}

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