What is the limit as x approaches-3-of (4-x^2)/(x+3) ?

The limit as x approaches-3-of (4-x^2)/(x+3) is infinity

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limit as x approaches-3-of (4-x^2)/(x+3)

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

\infty

Solution steps

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

\frac{4 - x ^{2}}{x + 3} = (4 - x^{2}) \frac{1}{x + 3}

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

x \to - 3 - lim (4 - x^{2}) = - 5

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

= (- 5) (- \infty)

Apply Infinity Property:

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

= \infty

x \to 0 lim (2 x csc (x))

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

x \to 0 lim (ln (sin (∣ x ∣)))

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

x \to - \infty lim (e^{x} - 2)

What is the limit as x approaches-3-of (4-x^2)/(x+3) ?
The limit as x approaches-3-of (4-x^2)/(x+3) is infinity