What is the limit as z approaches 2 of (z^3-8)/(z-2) ?

The limit as z approaches 2 of (z^3-8)/(z-2) is 12

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limit as z approaches 2 of (z^3-8)/(z-2)

z \to 2 lim (\frac{z ^{3} - 8}{z - 2})

12

Solution steps

z \to 2 lim (\frac{z ^{3} - 8}{z - 2})

Simplify

\frac{z ^{3} - 8}{z - 2} : z^{2} + 2 z + 4

= z \to 2 lim (z^{2} + 2 z + 4)

Plug in the value

z = 2

= 2^{2} + 2 \cdot 2 + 4

Simplify

= 12

x \to \frac{π}{2} + lim (\frac{tan ( x )}{x})

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

x \to 0 lim (\frac{3}{sin ( x )})

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

x \to - 2 - lim (\frac{x ^{2}}{3 x + 6})

What is the limit as z approaches 2 of (z^3-8)/(z-2) ?
The limit as z approaches 2 of (z^3-8)/(z-2) is 12