What is the limit as x approaches-4-of (x+2)/(x+4) ?

The limit as x approaches-4-of (x+2)/(x+4) is infinity

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limit as x approaches-4-of (x+2)/(x+4)

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

\infty

Solution steps

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

\frac{x + 2}{x + 4} = (x + 2) \frac{1}{x + 4}

= x \to - 4 - lim ((x + 2) \frac{1}{x + 4})

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 - 4 - lim (x + 2) \cdot x \to - 4 - lim (\frac{1}{x + 4})

x \to - 4 - lim (x + 2) = - 2

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

= (- 2) (- \infty)

Apply Infinity Property:

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

= \infty

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