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

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

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

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

\infty

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

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

= 2 \cdot 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

= 2 \cdot 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 2 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 0 - lim (\frac{e ^{- \frac{1}{x}}}{x})

x \to 3 - lim (\frac{1}{x})

x \to 0 lim (x^{x - 1})

x \to - 2 + lim (\frac{1}{( x + 2 ) ^{5}})

x \to \infty lim (45)

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