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Study23

  • 2 years ago

Please help me with this limit!!!

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  1. Study23
    • 2 years ago
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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. satellite73
    • 2 years ago
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    no you multiply out

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

  4. satellite73
    • 2 years ago
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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

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

  6. satellite73
    • 2 years ago
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    ?

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

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

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