What is the limit as x approaches 0 of (3-3e^{-x})/(e^x-1) ?

The limit as x approaches 0 of (3-3e^{-x})/(e^x-1) is 3

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limit as x approaches 0 of (3-3e^{-x})/(e^x-1)

x \to 0 lim (\frac{3 - 3 e ^{- x}}{e ^{x} - 1})

3

Solution steps

x \to 0 lim (\frac{3 - 3 e ^{- x}}{e ^{x} - 1})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{3 e ^{- x}}{e ^{x}})

= x \to 0 lim (\frac{3 e ^{- x}}{e ^{x}})

Plug in the value

x = 0

= \frac{3 e ^{- 0}}{e ^{0}}

Simplify

= 3

6 x^{5} + 4 e^{x}

x^{3} + y^{3} = 1

\int \frac{9 x ^{2}}{x ^{2} - 4} d x

x y^{^{'}} = y^{2} - y

y = \frac{x}{x - 5}

What is the limit as x approaches 0 of (3-3e^{-x})/(e^x-1) ?
The limit as x approaches 0 of (3-3e^{-x})/(e^x-1) is 3