What is the limit as x approaches infinity of 4xe^x ?

The limit as x approaches infinity of 4xe^x is infinity

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limit as x approaches infinity of 4xe^x

x \to \infty lim (4 x e^{x})

\infty

Solution steps

x \to \infty lim (4 x e^{x})

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

= 4 \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

= 4 \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

= 4 \cdot \infty \cdot \infty

Apply Infinity Property:

4\infty \infty = \infty

= \infty

x \to 0 - lim ([x])

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

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

x \to - 8 lim (f (x))

x \to 0 + lim (2 ln (x))

What is the limit as x approaches infinity of 4xe^x ?
The limit as x approaches infinity of 4xe^x is infinity