What is the limit as x approaches infinity of x^2e^{2x} ?

The limit as x approaches infinity of x^2e^{2x} is infinity

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limit as x approaches infinity of x^2e^{2x}

x \to \infty lim (x^{2} e^{2 x})

\infty

Solution steps

x \to \infty lim (x^{2} e^{2 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^{2}) \cdot x \to \infty lim (e^{2 x})

x \to \infty lim (x^{2}) = \infty

x \to \infty lim (e^{2 x}) = \infty

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

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

y^{^{''}} - 3 y^{^{'}} + 2 y = 14 sin (2 x) + 18 cos (2 x)

\frac{d}{d x} (3 x^{5} - 2 x^{4} - 4 x^{3})

(y - x^{2} + y^{2}) d x - x d y = 0

\frac{d}{d x} (x ln (x^{6}))

What is the limit as x approaches infinity of x^2e^{2x} ?
The limit as x approaches infinity of x^2e^{2x} is infinity