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

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

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

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

\infty

Solution steps

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

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

= x \to 2 + lim ((x + 7) \frac{1}{x ^{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

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

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

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

= 9 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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