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

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

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

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

\infty

Solution steps

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

Divide by highest denominator power:

\frac{3 x - 2 - \frac{5}{x}}{1 - \frac{4}{x}}

= x \to \infty lim (\frac{3 x - 2 - \frac{5}{x}}{1 - \frac{4}{x}})

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 - 2 - \frac{5}{x} )}{lim _{x \to \infty} ( 1 - \frac{4}{x} )}

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

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

= \frac{\infty}{1}

Apply Infinity Property:

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

= \infty

x \to \infty lim (\frac{1}{3 x})

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

d er i v a t i v e \frac{5 - x}{( 4 x ^{2} + 1 ) ^{3}}

\frac{d P}{d t} = 5 Pt, P (1) = 6

\frac{d}{d x} (\frac{( 7 - 5 x )}{cos ( x )})

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