What is the limit as x approaches 0 of (9^x-1)/x ?

The limit as x approaches 0 of (9^x-1)/x is 2ln(3)

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limit as x approaches 0 of (9^x-1)/x

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

2 ln (3)

Decimal Notation

2.19722 \dots

Solution steps

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 10 lim ((3 x) (x - 12))

x \to 0 + lim (\frac{x}{e ^{- \frac{3}{x}}})

x \to 1 lim (\frac{[ x ] + 2}{3})

x \to π - lim (ln (x) sin (x))

x \to - 1 lim (3 x^{2} + 2 x - 5)

What is the limit as x approaches 0 of (9^x-1)/x ?
The limit as x approaches 0 of (9^x-1)/x is 2ln(3)