What is the limit as x approaches 8+of (x-9)/(x-8) ?

The limit as x approaches 8+of (x-9)/(x-8) is -infinity

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limit as x approaches 8+of (x-9)/(x-8)

x \to 8 + lim (\frac{x - 9}{x - 8})

- \infty

Solution steps

x \to 8 + lim (\frac{x - 9}{x - 8})

\frac{x - 9}{x - 8} = (x - 9) \frac{1}{x - 8}

= x \to 8 + lim ((x - 9) \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 (x - 9) \cdot x \to 8 + lim (\frac{1}{x - 8})

x \to 8 + lim (x - 9) = - 1

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

= (- 1) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

What is the limit as x approaches 8+of (x-9)/(x-8) ?
The limit as x approaches 8+of (x-9)/(x-8) is -infinity