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

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

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

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

- \infty

Solution steps

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

\frac{x ^{3} - 4}{x - 2} = (x^{3} - 4) \frac{1}{x - 2}

= x \to 2 - lim ((x^{3} - 4) \frac{1}{x - 2})

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^{3} - 4) \cdot x \to 2 - lim (\frac{1}{x - 2})

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

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

= 4 (- \infty)

Apply Infinity Property:

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

= - \infty

x \to 0 lim (\frac{8 sin ( x )}{x})

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

x \to \frac{1}{2} lim (12 + x - x^{2})

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

x \to 0 + lim (- 1 + ln (x) x)

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