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Help find this limit.

  1. Oct 16, 2011 #1
    1. The problem statement, all variables and given/known data
    limit as h approaches 0


    2. Relevant equations
    lim h→0 [ 2(x+h)^5 -5(x+h)^3 - 2x^5 + 5x^3 ] / h


    3. The attempt at a solution
    People have told me to use the power rule and gave me an answer of 10 x^4 + 15 x^2 but that doesn't seem to be right...
     
  2. jcsd
  3. Oct 16, 2011 #2

    Mark44

    Staff: Mentor

    The answer they gave you is a little off. Assuming that your function is f(x) = 2x5 - 5x3, then f'(x) = 10x4 - 15x2.

    If the problem is to find the derivative using the limit definition of the derivative, then your friends' advice of using the power rule is also incorrect. To evaluate the limit you show, expand the first two terms. You should find that some terms drop out, and you can then take the limit.
     
  4. Oct 16, 2011 #3

    SammyS

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    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    In general: [itex]a^{n+1}-b^{n+1}=(a-b)(a^{n}+a^{n-1}b+a^{n-1}b^{2}+\dots+a^{n-k}b^{k}+\dots+a^{2}b^{n+2}+a\,b^{n-1}+b^{n})[/itex]

    So in specific, if n = 4, [itex]a^{5}-b^{5}=(a-b)(a^{4}+a^{3}b+a^{2}b^{2}+a\,b^{3}+b^{4})[/itex]

    If n = 2, [itex]a^{3}-b^{3}=(a-b)(a^{2}+a\,b+b^{2})[/itex]

    Now, let a = x+h, and b = x.
     
  5. Oct 16, 2011 #4
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