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

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

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

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

- \infty

Solution steps

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

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

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

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

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

= 1 \cdot (- \infty)

Apply Infinity Property:

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

= - \infty

x \to 3 lim (4 - 2 x)

x \to 0 lim (1 0^{x + 2})

x \to - 3 lim (x^{3} + 27)

x \to 2 lim (\frac{2 x}{4 - x ^{2}})

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

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