What is the limit as x approaches-10-of (x+9)/(x+10) ?

The limit as x approaches-10-of (x+9)/(x+10) is infinity

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limit as x approaches-10-of (x+9)/(x+10)

x \to - 10 - lim (\frac{x + 9}{x + 10})

\infty

Solution steps

x \to - 10 - lim (\frac{x + 9}{x + 10})

\frac{x + 9}{x + 10} = (x + 9) \frac{1}{x + 10}

= x \to - 10 - lim ((x + 9) \frac{1}{x + 10})

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 - 10 - lim (x + 9) \cdot x \to - 10 - lim (\frac{1}{x + 10})

x \to - 10 - lim (x + 9) = - 1

x \to - 10 - lim (\frac{1}{x + 10}) = - \infty

= (- 1) (- \infty)

Apply Infinity Property:

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

= \infty

What is the limit as x approaches-10-of (x+9)/(x+10) ?
The limit as x approaches-10-of (x+9)/(x+10) is infinity