What is the limit as x approaches 2-of (3x)/(x^2-4) ?

The limit as x approaches 2-of (3x)/(x^2-4) is -infinity

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limit as x approaches 2-of (3x)/(x^2-4)

x \to 2 - lim (\frac{3 x}{x ^{2} - 4})

- \infty

Solution steps

x \to 2 - lim (\frac{3 x}{x ^{2} - 4})

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

= 3 \cdot x \to 2 - lim (\frac{x}{x ^{2} - 4})

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

= 3 \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

= 3 \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

= 3 \cdot 2 (- \infty)

Apply Infinity Property:

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

= - \infty

\frac{d}{d x} (\frac{e ^{x}}{3 x ^{2} + 2 x ^{4}})

\frac{\partial}{\partial x} (2 x sin (8 x^{2} y))

y^{^{'}} = 0.0012 y (1700 - y)

y^{^{'}} = \frac{( 2 x ^{2} + 3 y ^{2} )}{2 x y}

\frac{\partial}{\partial v} (tan (\frac{u}{v}))

What is the limit as x approaches 2-of (3x)/(x^2-4) ?
The limit as x approaches 2-of (3x)/(x^2-4) is -infinity