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

The limit as x approaches 3 of (2-x)e^x is -e^3

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limit as x approaches 3 of (2-x)e^x

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

- e^{3}

Decimal

- 20.08553 \dots

Solution steps

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

Plug in the value

x = 3

= (2 - 3) e^{3}

Simplify

= - e^{3}

x \to 3 lim (2 x^{2} + 2 x - 12)

x \to 3 lim (x^{2} sin (\frac{1}{x}))

x \to 3 lim (\frac{1}{( 1 - x ) ^{4}})

x \to 3 lim ((\frac{x}{x + 1})^{x})

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

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