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

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

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

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

- \infty

Solution steps

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

\frac{x}{x ^{2} - 4} = x \frac{1}{x ^{2} - 4}

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

x \to - 2 - lim (x) = - 2

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

= (- 2) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

\frac{y}{2}

\frac{d}{d x} (- \frac{48 x}{( x ^{2} + 12 ) ^{2}})

\int e^{i x} d x

\frac{1}{sin ( x )}

\int sin (2 θ) sin (6 θ) d θ

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