What is the limit as x approaches infinity of 3xe^x ?

The limit as x approaches infinity of 3xe^x is infinity

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limit as x approaches infinity of 3xe^x

x \to \infty lim (3 x e^{x})

\infty

Solution steps

x \to \infty lim (3 x e^{x})

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

= 3 \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

= 3 \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

= 3 \cdot \infty \cdot \infty

Apply Infinity Property:

3\infty \infty = \infty

= \infty

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

y \to 1 lim (\frac{y ^{11} + 2 y - 3}{y ^{7} + y ^{2} - y - 1})

x \to 1 lim (3 x + 2)

x \to 1 lim (3 x^{2} - 7 x + 2)

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

What is the limit as x approaches infinity of 3xe^x ?
The limit as x approaches infinity of 3xe^x is infinity