What is the limit as x approaches 0 of ((3e^{-x}-3))/(x^2-2x) ?

The limit as x approaches 0 of ((3e^{-x}-3))/(x^2-2x) is 3/2

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limit as x approaches 0 of ((3e^{-x}-3))/(x^2-2x)

x \to 0 lim (\frac{( 3 e ^{- x} - 3 )}{x ^{2} - 2 x})

\frac{3}{2}

Decimal Notation

1.5

Solution steps

x \to 0 lim (\frac{3 e ^{- x} - 3}{x ^{2} - 2 x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- 3 e ^{- x}}{2 x - 2})

= x \to 0 lim (\frac{- 3 e ^{- x}}{2 x - 2})

Plug in the value

x = 0

= \frac{- 3 e ^{- 0}}{2 \cdot 0 - 2}

Simplify

\frac{- 3 e ^{- 0}}{2 \cdot 0 - 2} : \frac{3}{2}

= \frac{3}{2}

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What is the limit as x approaches 0 of ((3e^{-x}-3))/(x^2-2x) ?
The limit as x approaches 0 of ((3e^{-x}-3))/(x^2-2x) is 3/2