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

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

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

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

2

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= 2 \cdot \frac{1}{e ^{0}}

Simplify

2 \cdot \frac{1}{e ^{0}} : 2

= 2

\int \frac{1}{x ^{3} - 216} d x

x = - 2, x = 1, y = 10 x, y = x^{2} - 11

\frac{d}{d x} (\frac{x ^{4} - x ^{3} - 8}{( x - 3 ) ( x + 2 )})

y = x^{3} - 4, (2, 0)

\int_{0}^{2} (3 - x^{3}) d x

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