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

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

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

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

\infty

Solution steps

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

\frac{x + 2}{x + 6} = (x + 2) \frac{1}{x + 6}

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

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 - 6 - lim (x + 2) \cdot x \to - 6 - lim (\frac{1}{x + 6})

x \to - 6 - lim (x + 2) = - 4

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

= (- 4) (- \infty)

Apply Infinity Property:

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

= \infty

\int \frac{9}{x ^{2} - 9 x} d x

\frac{x}{1 + x ^{2}}

\int a x^{2} d x

5 - (x - 9)^{4}

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{7}{x ^{4}}) (x + 5 x^{3}))

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