What is the limit as x approaches infinity of xln(x) ?

The limit as x approaches infinity of xln(x) is infinity

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limit as x approaches infinity of xln(x)

x \to \infty lim (x ln (x))

\infty

Solution steps

x \to \infty lim (x ln (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 (ln (x))

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

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

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

f (x) = ((18 x (x^{2} + 6)^{8}))

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

\frac{d y}{d t} + 2 y = 3 t^{2} + 2 t - 1

n = 1 \sum \infty \frac{8 ^{n}}{n ^{4}}

\int_{0}^{\infty} \frac{1}{1 + e ^{x}} d x

What is the limit as x approaches infinity of xln(x) ?
The limit as x approaches infinity of xln(x) is infinity