What is the limit as x approaches infinity of (-3x^3+7x^2-6x+4)/(-3x^2+5x-5) ?

The limit as x approaches infinity of (-3x^3+7x^2-6x+4)/(-3x^2+5x-5) is infinity

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limit as x approaches infinity of (-3x^3+7x^2-6x+4)/(-3x^2+5x-5)

x \to \infty lim (\frac{- 3 x ^{3} + 7 x ^{2} - 6 x + 4}{- 3 x ^{2} + 5 x - 5})

\infty

Solution steps

x \to \infty lim (\frac{- 3 x ^{3} + 7 x ^{2} - 6 x + 4}{- 3 x ^{2} + 5 x - 5})

Divide by highest denominator power:

\frac{- 3 x + 7 - \frac{6}{x} + \frac{4}{x ^{2}}}{- 3 + \frac{5}{x} - \frac{5}{x ^{2}}}

= x \to \infty lim (\frac{- 3 x + 7 - \frac{6}{x} + \frac{4}{x ^{2}}}{- 3 + \frac{5}{x} - \frac{5}{x ^{2}}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to \infty} ( - 3 x + 7 - \frac{6}{x} + \frac{4}{x ^{2}} )}{lim _{x \to \infty} ( - 3 + \frac{5}{x} - \frac{5}{x ^{2}} )}

x \to \infty lim (- 3 x + 7 - \frac{6}{x} + \frac{4}{x ^{2}}) = - \infty

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

= \frac{- \infty}{- 3}

Apply Infinity Property:

\frac{- \infty}{- c} = \infty

= \infty

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

x \to 0 lim (\frac{sin ( - 2 x )}{x})

x \to 0 + lim ((1 + \frac{3}{x})^{2 x})

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

x \to 0 + lim (x^{π x})

What is the limit as x approaches infinity of (-3x^3+7x^2-6x+4)/(-3x^2+5x-5) ?
The limit as x approaches infinity of (-3x^3+7x^2-6x+4)/(-3x^2+5x-5) is infinity