What is the limit as x approaches 3-of (2-x)/(x-3) ?

The limit as x approaches 3-of (2-x)/(x-3) is infinity

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limit as x approaches 3-of (2-x)/(x-3)

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

\infty

Solution steps

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

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

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

x \to 3 - lim (2 - x) = - 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 (2-x)/(x-3) ?
The limit as x approaches 3-of (2-x)/(x-3) is infinity