1. Study23

$$\ \Huge \lim_{h \rightarrow 0} \ \frac{(2+h)^3-8}{h} .$$ Do I just multiply h/h, to get 1 on the denominator??

2. satellite73

no you multiply out

3. satellite73

$$(2+h)^3=...$$

4. satellite73

then subtract 8 and the usual miracle will occur everything without an $$h$$ will be gone, so you can factor an $$h$$ out of the numerator, cancel with the $$h$$ in the denominator, then replace $$h$$ by 0

5. Study23

How do I expand the trinomial?

6. satellite73

?

7. satellite73

if you do not know that $$(a+b)^2=a^3+3a^2b+3ab^2+a^3$$ then you have the annoying task of multiplying by hand $(2+h)(2+h)(2+h)$

8. satellite73

one more time $(a+b)^3=a^3+3a^2b+3ab^2+b^3$