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

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

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

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

2

Solution steps

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

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

= 2

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

x \to \infty lim (e^{- x} sin (e^{x}))

x \to 3 lim (\frac{2 x ^{2} - 10 x + 12}{x ^{2} + 3 x - 10})

x \to 0 lim (\frac{5 x + 3}{x})

x \to 4 + lim ((4 - x) \cdot ln (x - 4))

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