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

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

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

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

\infty

Solution steps

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

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

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

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

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

= (- 3) (- \infty)

Apply Infinity Property:

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

= \infty

x \to c lim (2 h (x) - 3 g (x))

x \to 0 lim (\frac{x}{2 - e ^{\frac{1}{x}}})

x \to 0 lim (3 (\frac{x}{sin ( x )}))

x \to π - lim (\frac{cos ( x )}{x})

x \to 0 lim (x^{2} + cos (x))

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