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 (- \infty)

Apply Infinity Property:

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

= - \infty

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

x \to 0 lim (5 x^{x})

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

x \to 0 lim (x^{2} - 3 e^{x})

x \to 4 lim (2 x - 9)

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