What is the limit as x approaches 0 of x/(e^{5x)-1} ?

The limit as x approaches 0 of x/(e^{5x)-1} is 1/5

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limit as x approaches 0 of x/(e^{5x)-1}

x \to 0 lim (\frac{x}{e ^{5 x} - 1})

\frac{1}{5}

Decimal Notation

0.2

Solution steps

x \to 0 lim (\frac{x}{e ^{5 x} - 1})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{5 e ^{5 x}})

= x \to 0 lim (\frac{1}{5 e ^{5 x}})

Plug in the value

x = 0

= \frac{1}{5 e ^{5 \cdot 0}}

Simplify

= \frac{1}{5}

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What is the limit as x approaches 0 of x/(e^{5x)-1} ?
The limit as x approaches 0 of x/(e^{5x)-1} is 1/5