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 Notation

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})

= 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)

f (x) = \frac{- 4 x ^{2} + 3 x - 7}{2 x ^{2} - 10 x - 3}

\int \frac{1}{x ( x ^{2} + 5 )} d x

\int - e^{- k t} k M d t

\frac{\partial}{\partial x} (arctan (x y) - z)

x \to 0 lim (- 3 (- 6) + 3 (- 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)