What is the limit as z approaches 2+of (z+7)/(z^2-4) ?

The limit as z approaches 2+of (z+7)/(z^2-4) is infinity

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limit as z approaches 2+of (z+7)/(z^2-4)

z \to 2 + lim (\frac{z + 7}{z ^{2} - 4})

\infty

Solution steps

z \to 2 + lim (\frac{z + 7}{z ^{2} - 4})

\frac{z + 7}{z ^{2} - 4} = (z + 7) \frac{1}{z ^{2} - 4}

= z \to 2 + lim ((z + 7) \frac{1}{z ^{2} - 4})

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

= z \to 2 + lim (z + 7) \cdot z \to 2 + lim (\frac{1}{z ^{2} - 4})

z \to 2 + lim (z + 7) = 9

z \to 2 + lim (\frac{1}{z ^{2} - 4}) = \infty

= 9 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 0 lim (- \frac{2}{x ^{2}})

x \to - 1 lim (\frac{x - 2}{x ^{3} - 8})

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

x \to 0 lim (\frac{2 x ^{2} - ∣ x ∣}{x})

x \to 2 lim (\frac{( 5 x - 5 )}{5})

What is the limit as z approaches 2+of (z+7)/(z^2-4) ?
The limit as z approaches 2+of (z+7)/(z^2-4) is infinity