Find the following limit:
lim_(h->0) ((h+3)^3-27)/h
((h+3)^3-27)/h = h^2+9 h+27:
lim_(h->0) (h^2+9 h+27)
lim_(h->0) (h^2+9 h+27) = 27+9 0+0^2 = 27:
Answer: |27
+118654 Evaluate the following limit: lim h→0 ((3+h)^3−27)/h
\(\displaystyle\lim_{h \rightarrow 0}\;\frac{(3+h)^3-27}{h}\\~\\ =\displaystyle\lim_{h \rightarrow 0}\;\frac{(3+h)^3-3^3}{h}\qquad note:\;a^3-b^3=(a-b)(a^2+ab+b^2)\\~\\ =\displaystyle\lim_{h \rightarrow 0}\;\frac{((3+h)-3)((3+h)^2+(3+h)*3+3^2)}{h}\\~\\ =\displaystyle\lim_{h \rightarrow 0}\;\frac{h[(3+h)^2+3(3+h)+9]}{h}\\~\\ =\displaystyle\lim_{h \rightarrow 0}\;\:(3+h)^2+3(3+h)+9\\~\\ =9+9+9\\~\\ =27 \)
