What is the limit as x approaches-7-of (x+3)/(x+7) ?

The limit as x approaches-7-of (x+3)/(x+7) is infinity

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limit as x approaches-7-of (x+3)/(x+7)

x \to - 7 - lim (\frac{x + 3}{x + 7})

\infty

Solution steps

x \to - 7 - lim (\frac{x + 3}{x + 7})

\frac{x + 3}{x + 7} = (x + 3) \frac{1}{x + 7}

= x \to - 7 - lim ((x + 3) \frac{1}{x + 7})

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 - 7 - lim (x + 3) \cdot x \to - 7 - lim (\frac{1}{x + 7})

x \to - 7 - lim (x + 3) = - 4

x \to - 7 - lim (\frac{1}{x + 7}) = - \infty

= (- 4) (- \infty)

Apply Infinity Property:

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

= \infty

What is the limit as x approaches-7-of (x+3)/(x+7) ?
The limit as x approaches-7-of (x+3)/(x+7) is infinity