What is the limit as x approaches infinity of 2g(x)x ?

The limit as x approaches infinity of 2g(x)x is infinity

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limit as x approaches infinity of 2g(x)x

x \to \infty lim (2 g (x) x)

\infty

Solution steps

x \to \infty lim (2 g (x) x)

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

= 2 \cdot x \to \infty lim (g (x) 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

= 2 \cdot x \to \infty lim (g (x)) \cdot x \to \infty lim (x)

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

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

= 2 g \cdot \infty \cdot \infty

Simplify

2 g \cdot \infty \cdot \infty : \infty

= \infty

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What is the limit as x approaches infinity of 2g(x)x ?
The limit as x approaches infinity of 2g(x)x is infinity