What is the limit as x approaches 0 of (4x)/(e^x-1) ?

The limit as x approaches 0 of (4x)/(e^x-1) is 4

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limit as x approaches 0 of (4x)/(e^x-1)

x \to 0 lim (\frac{4 x}{e ^{x} - 1})

4

Solution steps

x \to 0 lim (\frac{4 x}{e ^{x} - 1})

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

= 4 \cdot x \to 0 lim (\frac{x}{e ^{x} - 1})

Apply L'Hopital's Rule

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

= 4 \cdot x \to 0 lim (\frac{1}{e ^{x}})

Plug in the value

x = 0

= 4 \cdot \frac{1}{e ^{0}}

Simplify

4 \cdot \frac{1}{e ^{0}} : 4

= 4

x \to 1 lim (x^{2} - 4 x + 5)

x \to 2 + lim (\frac{3 x + 1}{2 - x})

x \to 0 lim ((1 - cos (x))^{x})

x \to 1 lim (x - 4)

x \to 0 lim (ln (ln (x)))

What is the limit as x approaches 0 of (4x)/(e^x-1) ?
The limit as x approaches 0 of (4x)/(e^x-1) is 4