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Finding residual

  1. Jun 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Given the following working, what steps must be taken to determine the values of the residuals A, B, and C?

    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Jun 14, 2012 #2

    HallsofIvy

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    You have
    [tex]\frac{7}{s(s- 2)^2}= \frac{A}{s}+ \frac{B}{s- 2}+ \frac{C}{(s- 2)^2}[/tex]

    Multiply on both sides by [itex]s(s- 2)^2[/itex] to get
    [tex]7= A(s- 2)^2+ Bs(s- 2)+ Cs[/tex]

    Now you can
    1) multiply the right side and combine "like powers of s":
    [tex]7= As^2+ 4As+ 4A+ Bs^2- 2Bs+ Cs= (A+ B)s^2+ (4A- 2B+ C)s+ 4A[/tex]
    for all s so we must have A+ B= 0, 4A- 2B= 0, and 4= 7, three equations to solve for A, B, and C.
    or
    2) Choose any three values for s you want so as to get three equations to solve for A, B, and C. For example, since we have the term s-2, taking s= 2 reduces to just 2C= 7. Since we have the term s, taking s= 0 reduces to 4A= 7. Taking s= 1, just because it is an easy number, A- B+ C= 7.
     
  4. Jun 14, 2012 #3
    thanks
     
  5. Jun 14, 2012 #4
    why was the right most term duplicated onto the LHS?
    EDIT: nevermind, i worked it out
     
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