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

The limit as x approaches-infinity of (x-8)/(x^2+6) is 0

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

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

0

Solution steps

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

Divide by highest denominator power:

\frac{\frac{1}{x} - \frac{8}{x ^{2}}}{1 + \frac{6}{x ^{2}}}

= x \to - \infty lim (\frac{\frac{1}{x} - \frac{8}{x ^{2}}}{1 + \frac{6}{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} ( \frac{1}{x} - \frac{8}{x ^{2}} )}{lim _{x \to - \infty} ( 1 + \frac{6}{x ^{2}} )}

x \to - \infty lim (\frac{1}{x} - \frac{8}{x ^{2}}) = 0

x \to - \infty lim (1 + \frac{6}{x ^{2}}) = 1

= \frac{0}{1}

Apply rule

\frac{0}{a} = 0, a \neq = 0

= 0

\frac{d}{d x} (\frac{d y}{d x}) + y = - 1

\int (e^{x} + e) d x

\frac{\partial}{\partial x} (- (x - 2) (y - 2) (x + y - 3))

\int \frac{4 x}{3 x ^{2} - 1} d x

\frac{\partial}{\partial x} (e^{- 4 x})

What is the limit as x approaches-infinity of (x-8)/(x^2+6) ?
The limit as x approaches-infinity of (x-8)/(x^2+6) is 0