What is the limit as x approaches 0 of x/(e^{7x)-1} ?

The limit as x approaches 0 of x/(e^{7x)-1} is 1/7

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limit as x approaches 0 of x/(e^{7x)-1}

x \to 0 lim (\frac{x}{e ^{7 x} - 1})

\frac{1}{7}

Decimal Notation

0.14285 \dots

Solution steps

x \to 0 lim (\frac{x}{e ^{7 x} - 1})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{7 e ^{7 x}})

= x \to 0 lim (\frac{1}{7 e ^{7 x}})

Plug in the value

x = 0

= \frac{1}{7 e ^{7 \cdot 0}}

Simplify

= \frac{1}{7}

y^{^{'}} + 4 y = 32

x \to 3 lim (3)

\frac{e ^{- s}}{s ^{2} + s}

(sin (x^{3}))^{^{'}}

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

What is the limit as x approaches 0 of x/(e^{7x)-1} ?
The limit as x approaches 0 of x/(e^{7x)-1} is 1/7