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

n \to \infty lim (- 5)

x \to - 6 lim (x^{2} + 7 x^{- 2})

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

x \to 0 - lim (4 (csc (x) - \frac{1}{x}))

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

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