What is the limit as x approaches-infinity of x*e^{1/x} ?

The limit as x approaches-infinity of x*e^{1/x} is -infinity

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limit as x approaches-infinity of x*e^{1/x}

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

- \infty

Solution steps

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

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^{\frac{1}{x}})

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

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

= (- \infty) \cdot 1

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

\int 4 t^{2} + 1 d t

x \to 0 lim (- ∣ x - 2 ∣ + 3)

\frac{\partial}{\partial x} (\frac{x + y}{x \cdot y})

\frac{d}{d x} (lo g_{3} (4 x))

\frac{d}{d θ} (\frac{8}{2 + cot ( θ ) sin ( θ )})

What is the limit as x approaches-infinity of x*e^{1/x} ?
The limit as x approaches-infinity of x*e^{1/x} is -infinity