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 (- \infty)

Apply Infinity Property:

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

= - \infty

\int (1 + x^{2}) \cdot 1 + 64 x^{2} d x

f (x) = 4 sec (x), at x = \frac{π}{6}

(2 y^{2} x + 3 x) d x + (2 x^{2} y) d y = 0

\frac{\partial}{\partial v} (\frac{v ^{2}}{u})

\frac{d}{d x} (2 - x - y + 1)

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