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

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

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

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

- 1

Solution steps

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

Simplify

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

= - 1

\frac{d}{d x} y = x^{3} (2 - x^{2})

y = x^{0.95}

a^{4} + cos^{4} (x)

\int_{0}^{1} y d y

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