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Study23 Group Title

Please help me with this limit!!!

  • 2 years ago
  • 2 years ago

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  1. Study23 Group Title
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    \(\ \Huge \lim_{h \rightarrow 0} \ \frac{(2+h)^3-8}{h} .\) Do I just multiply h/h, to get 1 on the denominator??

    • 2 years ago
  2. satellite73 Group Title
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    no you multiply out

    • 2 years ago
  3. satellite73 Group Title
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    \((2+h)^3=...\)

    • 2 years ago
  4. satellite73 Group Title
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    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

    • 2 years ago
  5. Study23 Group Title
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    How do I expand the trinomial?

    • 2 years ago
  6. satellite73 Group Title
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    ?

    • 2 years ago
  7. satellite73 Group Title
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    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 \[(2+h)(2+h)(2+h)\]

    • 2 years ago
  8. satellite73 Group Title
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    one more time \[(a+b)^3=a^3+3a^2b+3ab^2+b^3\]

    • 2 years ago
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