What is the limit as x approaches 0 of (3^{2x}-1)/x ?

The limit as x approaches 0 of (3^{2x}-1)/x is 2ln(3)

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limit as x approaches 0 of (3^{2x}-1)/x

x \to 0 lim (\frac{3 ^{2 x} - 1}{x})

2 ln (3)

Decimal Notation

2.19722 \dots

Solution steps

x \to 0 lim (\frac{3 ^{2 x} - 1}{x})

3^{2 x} = 9^{x}

= x \to 0 lim (\frac{9 ^{x} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{2 ln ( 3 ) \cdot 9 ^{x}}{1})

= x \to 0 lim (\frac{2 ln ( 3 ) \cdot 9 ^{x}}{1})

Plug in the value

x = 0

= \frac{2 ln ( 3 ) \cdot 9 ^{0}}{1}

Simplify

= 2 ln (3)

x \to - 1 lim (1 - 4 x)

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

x \to 2 lim (e^{x^{2} - 2})

x \to 3 lim (\frac{5 x + 3}{x - 1})

x \to 0 lim (\frac{cos ( x )}{1})

What is the limit as x approaches 0 of (3^{2x}-1)/x ?
The limit as x approaches 0 of (3^{2x}-1)/x is 2ln(3)