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Homework Help: Give a formula the open unit disk

  1. Mar 30, 2010 #1
    1. The problem statement, all variables and given/known data

    In the open unit disk D = {(x,y)|x2 + y2 < 1} give a forumla for:

    (a) [tex]\frac{\partial \sum ^{inf}_{n=0} (xy) ^{n}}{\partial x}[/tex]

    (b) [tex]\frac{\partial (e^{x+y} \int ^{y}_{x} e^{-t} dt)}{\partial y}[/tex]

    2. Relevant equations



    3. The attempt at a solution

    Ok this is on my exam review sheet and he gave us the solutions to go along with it.. I don't know if I wasn't paying attention in class or what but I don't remember doing anything like this.

    His first step for a is [tex]\sum ^{inf}_{n=0} (xy)^{n} = \frac{1}{1 - xy}[/tex] if xy < 1 (But for all (x,y)[tex]\in[/tex] D xy < 1

    I'm already confused at this point. Can someone please let me know what is going on here? Thanks
     
  2. jcsd
  3. Mar 30, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The sum of r^n is 1/(1-r) if |r|<1. Now put r=(xy). It's just a geometric series. For the second one just evaluate the integral and take the partial derivative using the product rule etc. There's nothing really special going on there.
     
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