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Does limit exist as x approaches zero? Frobenius Method DEQ

  1. Apr 13, 2013 #1
    1. The problem statement, all variables and given/known data

    what is the limit of (4x^2-1)/(4x^2)
    when x→0

    2. Relevant equations

    In order to find the Indicial Equation, do I need to take the limit of p(x) and q(x), the non-constant coefficients? If so, can the limit of this function be found using LH Rule?

    3. The attempt at a solution

    Please let me know any info you might have about the Frobenius Method, since I am just learning it from my professor's brief notes about it...
     
  2. jcsd
  3. Apr 13, 2013 #2

    LCKurtz

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    What do you think? What have you tried?
     
  4. Apr 13, 2013 #3
    Well, can you use L' Hopital's Rule twice? (8x - 0)/(8x) and then (8/8) = 1 ?

    But I'm confused if I need to multiple by x^2 to find q(nault)?

    x^2*q(x)=q(nault)

    y''(x) + p(x)y'(x) + q(x)y(x) = 0

    If so, would the limit be -1/4?

    x^2(4x^2-1)/(4x^2) = [(4x^4)/4x^2] - [x^2/(4x^2)] = [x^2] - [1/4] = [x=0] = - 1/4
     
    Last edited: Apr 13, 2013
  5. Apr 13, 2013 #4

    HallsofIvy

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    L'Hopital applies only when the numerator and denominator both go to 0. Here, if x= 0, the numerator is -1 but the denominator is 0. Suppose x were some very small number, say x= 0.000001. What would that fraction be? Now, what do you thing the limit is?
     
  6. Apr 13, 2013 #5
    negative infinity, right?
     
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