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Expand (b^2 + y^2)^(3/2) as a Taylor's series In terms of y/b

  1. Dec 6, 2014 #1
    1. The problem statement, all variables and given/known data


    Expand (b^2 + y^2)^(3/2) as a Taylor's series In terms of y/b


    2. Relevant equations


    3. The attempt at a solution

    Hello, I'm clueless on this one. I tried to factor out b^3 -> b^3(1 + y^3), but cant figure out what to do next.

    Thanks in advance.
     
  2. jcsd
  3. Dec 6, 2014 #2

    Mark44

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    Write b2 + y2 as b2(1 + y2/b2), and bring it out as (b2)3/2, or b3.
     
  4. Dec 7, 2014 #3

    vela

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    It looks like you did the following: ##(b^2 + y^2)^{3/2} = (b^2)^{3/2} + (y^2)^{3/2} = b^3 + y^3##. If so, don't do that. It's wrong.
     
  5. Dec 8, 2014 #4
    Sorry for the delay - This makes much more sense now. So, once you pull out the b^2, you have:

    (b^2 (1 + y^2 / b^2))^3/2 = b^3 (1 + y^3 / b^3) [b^3's cancel out] = (1 + y^3) ---> p = 1, and x = y^3, ready to be substituted into Binomial Series.

    Series:

    1 + px + p(p-1)x / 2!.... = 1 + y^3 + (y^3)(y^3 - 1) / 2! + (y^3)(y^3 - 1)(y^3 - (n - 1) / n!)
     
  6. Dec 8, 2014 #5

    vela

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    You really need to review basic algebra. First off, ##(a+b)^n \ne a^n + b^n##. Even if you could do that, the ##b^3##'s wouldn't cancel out.
     
  7. Dec 8, 2014 #6
    Thanks for the reply, but I really didn't see a need to insult me (simply telling me what I did wrong should be sufficient). I am pretty good at algebra (I've gotten A's in all of my Algebra classes). The problem is that my mind is focusing on making sure I understand the problem, and I may overlook some things, like basic factorization.
     
    Last edited: Dec 8, 2014
  8. Dec 8, 2014 #7

    vela

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    It wasn't meant as an insult; it was advice. You've made really basic algebra mistakes. You didn't factor the expression correctly in the original post; you incorrectly distributed the exponents; and you canceled terms you can't cancel. I'll note that I pointed out the mistake about the exponents in post 3, and you didn't seem to get what you did was wrong because you repeated the mistake in your subsequent post. Perhaps it was just a fluke, and you don't commonly make these types of errors. On the other hand, every step that you've written in this thread has had a major mistake in it.

    It would be one thing if you were currently taking algebra, but it appears you're in calculus because you're learning about the Taylor series. At this point, you really should have these basics down.
     
  9. Dec 8, 2014 #8

    Mark44

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    How is that an insult? If you're posting a calculus problem such as the one in this thread, and you make a number of conceptual errors at the algebra level, then clearly, vela's comment applies.
     
    Last edited by a moderator: Dec 8, 2014
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