What is the limit as x approaches infinity of x(1-x) ?

The limit as x approaches infinity of x(1-x) is -infinity

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limit as x approaches infinity of x(1-x)

x \to \infty lim (x (1 - x))

- \infty

Solution steps

x \to \infty lim (x (1 - 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 (1 - x)

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

x \to \infty lim (1 - x) = - \infty

= \infty \cdot (- \infty)

Apply Infinity Property:

\infty (- \infty) = - \infty

= - \infty

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

x \to 0 lim (\frac{1}{1 + 3 ^{\frac{1}{x}}})

x \to π + lim (- cot (x) csc (x))

x \to \infty lim (\frac{5}{7})

n \to \infty lim (n + 2)

What is the limit as x approaches infinity of x(1-x) ?
The limit as x approaches infinity of x(1-x) is -infinity