What is the limit as x approaches infinity of (x-x^4)/(1-x) ?

The limit as x approaches infinity of (x-x^4)/(1-x) is infinity

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limit as x approaches infinity of (x-x^4)/(1-x)

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

\infty

Solution steps

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

Simplify

\frac{x - x ^{4}}{1 - x} : x (x^{2} + x + 1)

= x \to \infty lim (x (x^{2} + x + 1))

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 (x^{2} + x + 1)

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

x \to \infty lim (x^{2} + x + 1) = \infty

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

n \to \infty lim (n (1 + 2^{n} + 3^{n}))

h \to 0 lim (\frac{( 3 - 9 + h )}{h})

x \to 2 lim ((x - 2) sin (\frac{1}{x - 2}))

x \to c lim (a x + b)

x \to - \infty lim (\frac{x ^{2} + 4}{x + 7})

What is the limit as x approaches infinity of (x-x^4)/(1-x) ?
The limit as x approaches infinity of (x-x^4)/(1-x) is infinity