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

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

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limit as x approaches-8-of (-5x+2)/(x+8)

x \to - 8 - lim (\frac{- 5 x + 2}{x + 8})

- \infty

Solution steps

x \to - 8 - lim (\frac{- 5 x + 2}{x + 8})

\frac{- 5 x + 2}{x + 8} = (- 5 x + 2) \frac{1}{x + 8}

= x \to - 8 - lim ((- 5 x + 2) \frac{1}{x + 8})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to - 8 - lim (- 5 x + 2) \cdot x \to - 8 - lim (\frac{1}{x + 8})

x \to - 8 - lim (- 5 x + 2) = 42

x \to - 8 - lim (\frac{1}{x + 8}) = - \infty

= 42 (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

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