What is the limit as x approaches infinity of (5x+6x^2)/(3x-8) ?

The limit as x approaches infinity of (5x+6x^2)/(3x-8) is infinity

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limit as x approaches infinity of (5x+6x^2)/(3x-8)

x \to \infty lim (\frac{5 x + 6 x ^{2}}{3 x - 8})

\infty

Solution steps

x \to \infty lim (\frac{5 x + 6 x ^{2}}{3 x - 8})

Divide by highest denominator power:

\frac{5 + 6 x}{3 - \frac{8}{x}}

= x \to \infty lim (\frac{5 + 6 x}{3 - \frac{8}{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} ( 5 + 6 x )}{lim _{x \to \infty} ( 3 - \frac{8}{x} )}

x \to \infty lim (5 + 6 x) = \infty

x \to \infty lim (3 - \frac{8}{x}) = 3

= \frac{\infty}{3}

Apply Infinity Property:

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

= \infty

\frac{1}{2}

x \to 5 lim (\frac{( x ^{4} - 625 )}{x - 5})

y^{^{'}} + 4 y^{2} e^{- 1 x} = 0, y (0) = 3

e^{3 t} cos (3 t)

\frac{\partial}{\partial y} (y^{2} e^{x y})

What is the limit as x approaches infinity of (5x+6x^2)/(3x-8) ?
The limit as x approaches infinity of (5x+6x^2)/(3x-8) is infinity