What is the limit as x approaches-2-of (3x-1)/(x+2) ?

The limit as x approaches-2-of (3x-1)/(x+2) is infinity

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limit as x approaches-2-of (3x-1)/(x+2)

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

\infty

Solution steps

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

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

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

x \to - 2 - lim (3 x - 1) = - 7

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

= (- 7) (- \infty)

Apply Infinity Property:

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

= \infty

What is the limit as x approaches-2-of (3x-1)/(x+2) ?
The limit as x approaches-2-of (3x-1)/(x+2) is infinity