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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

Simplify

= 1

\frac{d}{d x} (\frac{x ^{2}}{x ^{3}})

d er i v a t i v e e^{x} (x^{2} + 1) (x + 4)

a re a y = - x, y = - x^{2} + e x

p a r i t y \frac{csc ( 3 x )}{x ^{3}}

\int \frac{e ^{- x}}{x ^{3}} d x

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