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

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

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

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

2

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

= 2

\frac{d y}{d x} = 2 + e^{- 2 x + y + 1}

y = 2 x - 3 x^{2}

\frac{d}{d x} (cos^{3} (5 x))

\int_{0}^{1} \frac{2 t}{( 2 - t ) ^{2}} d t

\int \frac{x ^{3}}{x ^{2} - 9} d x

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