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

The limit as x approaches-infinity of f(x)x is infinity

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limit as x approaches-infinity of f(x)x

x \to - \infty lim (f (x) x)

\infty

Solution steps

x \to - \infty lim (f (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

= x \to - \infty lim (f (x)) \cdot x \to - \infty lim (x)

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

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

= f (- \infty) (- \infty)

Simplify

f (- \infty) (- \infty) : \infty

= \infty

x \to 0 + lim (\frac{1}{∣ ln ( x ) ∣})

x \to 0 + lim (x^{(e^{x} - 1)})

x \to 1 lim (5 x \cdot (1 + x))

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

x \to 0 + lim ((2 x)^{x^{2}})

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