What is the limit as x approaches 5-of (x-2)/(x-5) ?

The limit as x approaches 5-of (x-2)/(x-5) is -infinity

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limit as x approaches 5-of (x-2)/(x-5)

x \to 5 - lim (\frac{x - 2}{x - 5})

- \infty

Solution steps

x \to 5 - lim (\frac{x - 2}{x - 5})

\frac{x - 2}{x - 5} = (x - 2) \frac{1}{x - 5}

= x \to 5 - lim ((x - 2) \frac{1}{x - 5})

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 5 - lim (x - 2) \cdot x \to 5 - lim (\frac{1}{x - 5})

x \to 5 - lim (x - 2) = 3

x \to 5 - lim (\frac{1}{x - 5}) = - \infty

= 3 (- \infty)

Apply Infinity Property:

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

= - \infty

What is the limit as x approaches 5-of (x-2)/(x-5) ?
The limit as x approaches 5-of (x-2)/(x-5) is -infinity