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

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

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limit as x approaches infinity of xe^{3x}

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

\infty

Solution steps

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

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

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

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

x \to 0 lim (\frac{1 - co x}{x ^{2}})

x \to - 1 lim (8 + 3 x)

x \to - \infty lim (\frac{3 e ^{x} - 4 e ^{- x}}{2 e ^{x} + e ^{- x}})

x \to 8 lim (7 x + 9)

x \to \infty lim ((\frac{1}{3}) x)

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