What is the limit as x approaches-infinity of e^xx ?

The limit as x approaches-infinity of e^xx is 0

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limit as x approaches-infinity of e^xx

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

0

Solution steps

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

Rewrite for L'Hopital

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

Apply L'Hopital's Rule

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

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

Simplify

\frac{1}{- e ^{- x}} : - e^{x}

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

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

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

Apply the common limit:

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

= - 0

Simplify

= 0

x \to 14 lim (2)

x \to 0 lim (ln (x) x)

x \to \infty lim (\frac{e ^{5 x}}{3 - e ^{2 x}})

x \to 0 lim (x cos (2 x))

x \to 0 lim (sin (x) cos (x))

What is the limit as x approaches-infinity of e^xx ?
The limit as x approaches-infinity of e^xx is 0