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

\int_{- \infty}^{8} r e^{\frac{r}{2}} d r

\frac{d}{d t} (sin (π t))

\frac{\partial}{\partial y} (sin^{3} (x^{2} y))

\int_{- 1}^{1} (x^{2} + 1)^{2} d x

y = e^{- \frac{1}{2} 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