anonymous
  • anonymous
Please help me with this limit!!!
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\(\ \Huge \lim_{h \rightarrow 0} \ \frac{(2+h)^3-8}{h} .\) Do I just multiply h/h, to get 1 on the denominator??
anonymous
  • anonymous
no you multiply out
anonymous
  • anonymous
\((2+h)^3=...\)

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anonymous
  • anonymous
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
anonymous
  • anonymous
How do I expand the trinomial?
anonymous
  • anonymous
?
anonymous
  • anonymous
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 \[(2+h)(2+h)(2+h)\]
anonymous
  • anonymous
one more time \[(a+b)^3=a^3+3a^2b+3ab^2+b^3\]

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