What is the limit as x approaches 0 of (x^2)/(e^x-1) ?

The limit as x approaches 0 of (x^2)/(e^x-1) is 0

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limit as x approaches 0 of (x^2)/(e^x-1)

x \to 0 lim (\frac{x ^{2}}{e ^{x} - 1})

0

Solution steps

x \to 0 lim (\frac{x ^{2}}{e ^{x} - 1})

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 0

\int 3 sec (x) d x

\frac{\partial}{\partial x} (a^{2})

\int (x - 2)^{\frac{3}{2}} d x

x \to 7 - lim (\frac{2 x + 1}{x - 7})

x \to \infty lim (1.0 7^{x})

What is the limit as x approaches 0 of (x^2)/(e^x-1) ?
The limit as x approaches 0 of (x^2)/(e^x-1) is 0