What is the limit as x approaches infinity of 5xe^x ?

The limit as x approaches infinity of 5xe^x is infinity

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limit as x approaches infinity of 5xe^x

x \to \infty lim (5 x e^{x})

\infty

Solution steps

x \to \infty lim (5 x e^{x})

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

= 5 \cdot x \to \infty lim (x e^{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

= 5 \cdot x \to \infty lim (x) \cdot x \to \infty lim (e^{x})

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

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

= 5 \cdot \infty \cdot \infty

Apply Infinity Property:

5\infty \infty = \infty

= \infty

x \to 3 - lim (\frac{3 x}{x - 3})

x \to + 0 lim (sin (\frac{1}{x}))

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

x \to 1 lim (4 x^{2} - 13 x + 12)

x \to 0 lim (2 - 4 x + 7 x^{2})

What is the limit as x approaches infinity of 5xe^x ?
The limit as x approaches infinity of 5xe^x is infinity