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Homework Help: Linear approximation question of ##xy−5y^2##

  1. Sep 25, 2014 #1
    First, I already know that when we have to do linear approximation of ##f(x, y)## if ##\Delta z = f_{x}(a, b)\Delta x + f_{y}(a, b)\Delta y + \epsilon_{1}\Delta x + \epsilon_{2}\Delta y ##. and ##\epsilon_{1}## and ##\epsilon_{2}## approaches to nought wneh ##(\Delta x, \Delta y)## approaches zero. But how can I find appropriate value of ##\epsilon_{1}## and ##\epsilon_{2}##? in this question for example, epsilons of ##z = f(x, y) = xy-5y^2##?
     
  2. jcsd
  3. Sep 25, 2014 #2

    Mark44

    Staff: Mentor

    First off, do not delete the three parts of the template. They are there for a reason.

    The formula you show for ##\Delta z## gives the exact change in z (or in your case, f). What you're after is a linear approximation, so you can ignore the two terms with ##\epsilon##.
     
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