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

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

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

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

2 ln (a)

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

= 2 ln (a)

x \to 7 lim (\frac{1}{x ^{2} ( x + 7 )})

\frac{d}{d x} (a cos (2 x))

\int \frac{x}{x ^{2} + 8 x} d x

y = a x^{3}

\int_{0}^{1} \frac{ln ( t )}{t} d t

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