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

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

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

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

- \infty

Solution steps

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

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

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

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

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

= (- 3) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

x \to 0 + lim (arccot (\frac{1}{x}))

x \to 1 + lim (4 x - 4)

x \to 2 + lim (\frac{x ^{2} + 1}{x + 2})

x \to - 20 lim (\frac{1}{2 x})

x \to 4 lim (3 ∣ x - 1 ∣)

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