What is the limit as h approaches 0 of ((h-2)^3+8)/h ?

The limit as h approaches 0 of ((h-2)^3+8)/h is 12

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limit as h approaches 0 of ((h-2)^3+8)/h

h \to 0 lim (\frac{( h - 2 ) ^{3} + 8}{h})

12

Solution steps

h \to 0 lim (\frac{( h - 2 ) ^{3} + 8}{h})

Simplify

\frac{( h - 2 ) ^{3} + 8}{h} : h^{2} - 6 h + 12

= h \to 0 lim (h^{2} - 6 h + 12)

Plug in the value

h = 0

= 0^{2} - 6 \cdot 0 + 12

Simplify

= 12

What is the limit as h approaches 0 of ((h-2)^3+8)/h ?
The limit as h approaches 0 of ((h-2)^3+8)/h is 12