What is the limit as x approaches-infinity of x-3x^4 ?

The limit as x approaches-infinity of x-3x^4 is -infinity

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limit as x approaches-infinity of x-3x^4

x \to - \infty lim (x - 3 x^{4})

- \infty

Solution steps

x \to - \infty lim (x - 3 x^{4})

Apply Infinity Property:

x \to \pm \infty lim (a x^{n} + \dots + b x + c) = - \infty, a < 0,

n is even

a = - 3, n = 4

= - \infty

x \to 0 + lim (2 x ln (\frac{1}{x}))

x \to \frac{1}{4} lim (ln (x))

x \to 0 lim (1 - 5 x^{3})

x \to 0 lim (\frac{x ^{4} - 2}{x ^{3}})

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

What is the limit as x approaches-infinity of x-3x^4 ?
The limit as x approaches-infinity of x-3x^4 is -infinity