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

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

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

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

2 ln (a)

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

= 2 ln (a)

\int_{1}^{12} \frac{1}{x - 10} d x

\frac{\partial}{\partial x} (\frac{e ^{x}}{x ^{2} + 10})

n = 0 \sum \infty \frac{2 n + 1}{n !}

- 2 e^{x + 2} + e^{- 5}

y^{^{'}} = \frac{4 x ^{5} e ^{\frac{y}{x}} + x ^{3} y ^{2}}{x ^{4} y}

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