What is the limit as x approaches 2-of (2x+1)/(x-2) ?

The limit as x approaches 2-of (2x+1)/(x-2) is -infinity

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limit as x approaches 2-of (2x+1)/(x-2)

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

- \infty

Solution steps

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

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

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

x \to 2 - lim (2 x + 1) = 5

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

= 5 (- \infty)

Apply Infinity Property:

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

= - \infty

What is the limit as x approaches 2-of (2x+1)/(x-2) ?
The limit as x approaches 2-of (2x+1)/(x-2) is -infinity