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

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

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

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

0

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{3 x ^{2}}{e ^{x}})

= x \to 0 lim (\frac{3 x ^{2}}{e ^{x}})

Plug in the value

x = 0

= \frac{3 \cdot 0 ^{2}}{e ^{0}}

Simplify

\frac{3 \cdot 0 ^{2}}{e ^{0}} : 0

= 0

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\int 20 + 75 e^{- \frac{x}{50}} d x

5 x^{2}

n = 1 \sum \infty (- 3)^{3 n - 1}

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