What is the limit as x approaches 3-of (7-x-5)/(x-3) ?

The limit as x approaches 3-of (7-x-5)/(x-3) is infinity

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limit as x approaches 3-of (7-x-5)/(x-3)

x \to 3 - lim (\frac{7 - x - 5}{x - 3})

\infty

Solution steps

x \to 3 - lim (\frac{7 - x - 5}{x - 3})

Simplify

= x \to 3 - lim (\frac{- x + 2}{x - 3})

\frac{- x + 2}{x - 3} = (- x + 2) \frac{1}{x - 3}

= x \to 3 - lim ((- x + 2) \frac{1}{x - 3})

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 3 - lim (- x + 2) \cdot x \to 3 - lim (\frac{1}{x - 3})

x \to 3 - lim (- x + 2) = - 1

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

= (- 1) (- \infty)

Apply Infinity Property:

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

= \infty

What is the limit as x approaches 3-of (7-x-5)/(x-3) ?
The limit as x approaches 3-of (7-x-5)/(x-3) is infinity