What is the limit as x approaches 2+of (x-13)/(-x+2) ?

The limit as x approaches 2+of (x-13)/(-x+2) is infinity

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limit as x approaches 2+of (x-13)/(-x+2)

x \to 2 + lim (\frac{x - 13}{- x + 2})

\infty

Solution steps

x \to 2 + lim (\frac{x - 13}{- x + 2})

\frac{x - 13}{- x + 2} = (x - 13) \frac{1}{- x + 2}

= x \to 2 + lim ((x - 13) \frac{1}{- x + 2})

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 2 + lim (x - 13) \cdot x \to 2 + lim (\frac{1}{- x + 2})

x \to 2 + lim (x - 13) = - 11

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

= (- 11) (- \infty)

Apply Infinity Property:

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

= \infty

What is the limit as x approaches 2+of (x-13)/(-x+2) ?
The limit as x approaches 2+of (x-13)/(-x+2) is infinity