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

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

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

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

- \infty

Solution steps

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

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

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

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

x \to - 3 + lim (x - 3) = - 6

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

= (- 6) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

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

x \to 5 lim (3 x + 1)

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

x \to - 2 lim (2 x^{3} - x^{2} + 4 x + 1)

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

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