What is the limit as n approaches infinity of nx^n ?

The limit as n approaches infinity of nx^n is Undefined

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limit as n approaches infinity of nx^n

n \to \infty lim (n x^{n})

Undefined

Solution steps

n \to \infty lim (n x^{n})

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

= n \to \infty lim (n) \cdot n \to \infty lim (x^{n})

n \to \infty lim (n) = \infty

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

Undefined

= \infty \cdot Undefined

= Undefined

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

x \to 0 lim (\frac{arctan ( x ) - arcsin ( x )}{x ( 1 - cos ( x ) )})

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

x \to 2 lim (\frac{x ^{2} + 5}{x - 3})

x \to 1 + lim (x^{\frac{1}{x ^{4} - 1}})

What is the limit as n approaches infinity of nx^n ?
The limit as n approaches infinity of nx^n is Undefined