What is the limit as x approaches-infinity of xe^{-x+2} ?

The limit as x approaches-infinity of xe^{-x+2} is -infinity

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limit as x approaches-infinity of xe^{-x+2}

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

- \infty

Solution steps

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to - \infty lim (x) \cdot x \to - \infty lim (e^{- x + 2})

x \to - \infty lim (x) = - \infty

x \to - \infty lim (e^{- x + 2}) = \infty

= (- \infty) \cdot \infty

Apply Infinity Property:

(- \infty) \infty = - \infty

= - \infty

\frac{\partial}{\partial x} (ln (x + 3 y + 4 z))

\int \frac{x ^{2}}{( 3 x + 1 ) ^{3}} d x

\frac{d}{d x} ((5 x)^{\frac{1}{2}})

\frac{d}{d x} (x cos (π x) + 1)

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = 0

What is the limit as x approaches-infinity of xe^{-x+2} ?
The limit as x approaches-infinity of xe^{-x+2} is -infinity