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

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

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

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

ln (3)

Decimal

1.09861 \dots

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

Simplify

= ln (3)

\int_{0}^{6} π (36 x^{2} - x^{4}) d x

x \to 0 lim ((ln (x))^{x})

\int \frac{x}{x - 3} d x

\int \frac{1}{2} cos (x) d x

\frac{d}{d x} (\frac{3 x}{x ^{3} + 7 x - 5})

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