What is the limit as x approaches infinity-of ((8x^3+6x+7))/((6x-7)) ?

The limit as x approaches infinity-of ((8x^3+6x+7))/((6x-7)) is infinity

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limit as x approaches infinity-of ((8x^3+6x+7))/((6x-7))

x \to \infty - lim (\frac{( 8 x ^{3} + 6 x + 7 )}{( 6 x - 7 )})

\infty

Solution steps

x \to \infty lim (\frac{8 x ^{3} + 6 x + 7}{6 x - 7})

Divide by highest denominator power:

\frac{8 x ^{2} + 6 + \frac{7}{x}}{6 - \frac{7}{x}}

= x \to \infty lim (\frac{8 x ^{2} + 6 + \frac{7}{x}}{6 - \frac{7}{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} ( 8 x ^{2} + 6 + \frac{7}{x} )}{lim _{x \to \infty} ( 6 - \frac{7}{x} )}

x \to \infty lim (8 x^{2} + 6 + \frac{7}{x}) = \infty

x \to \infty lim (6 - \frac{7}{x}) = 6

= \frac{\infty}{6}

Apply Infinity Property:

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

= \infty

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What is the limit as x approaches infinity-of ((8x^3+6x+7))/((6x-7)) ?
The limit as x approaches infinity-of ((8x^3+6x+7))/((6x-7)) is infinity