Answer
$$\lim\limits_{h\to0}\frac{(h-1)^3+1}{h}=3$$
Work Step by Step
$$A=\lim\limits_{h\to0}\frac{(h-1)^3+1}{h}$$
- Consider the numerator:
$(h-1)^3+1=(h^3-3h^2+3h-1)+1=h^3-3h^2+3h=h(h^2-3h+3)$
Therefore, $$A=\lim\limits_{h\to0}\frac{h(h^2-3h+3)}{h}$$$$A=\lim\limits_{h\to0}(h^2-3h+3)$$$$A=0^2-3\times0+3$$$$A=3$$
