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

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

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

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

3

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{3 e ^{3 \cdot 0}}{1}

Simplify

= 3

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

\int \frac{s ^{2}}{s ^{3} + 5} d s

\frac{d}{d x} (\frac{x}{x - 1} - \frac{1}{ln ( x )})

y = x^{2} + 3, (- 5, 28)

f (x) = x^{2} + x

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