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

x \to π lim (cos (x + cos (x)))

x \to 0 lim (\frac{1 - cos ( 8 x )}{1 - cos ( 3 x )})

x \to 3 lim ((x - 3)^{x - 3})

x \to 0 lim (e^{c o s (x)})

x \to x lim (e^{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