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Multivar Calc

  1. Oct 26, 2005 #1
    8. Let f : R^3 → R a function all whose first order partial derivatives are continuous and such that f(0, 1, 1) = 0,
    f_x(0, 1, 1) = 1, f_y(0, 1, 1) = 2, f_z(0, 1, 1) = 3. Find lim
    t-->0
    f(t2, cosh t, et)
    f(t, cos t, cosh t)

    9. Let f : R2 → R such that f(x, y) = f(y,−x) for all (x, y) ∈ R2, and f(2, y) = 2 + |y|. Then
    A f_x(1, 2) = 1
    B f_x(1, 2) = 0
    C f_x(0, 2) = 1
    D f_x(0, 2) = −1
    E none of these

    Hey. These are two problems on a practise test. I have no clue whatsoever how to do the first. My question for the second: does f(x,y) mean the same thing as f(y,x)?

    Thanks so much.
     
    Last edited: Oct 26, 2005
  2. jcsd
  3. Oct 26, 2005 #2

    James R

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    Science Advisor
    Homework Helper
    Gold Member

    When you see f(x,y)=f(y,-x), the x and y are place holders.

    For example, this statement says that

    f(1,2) = f(2,-1)
    f(3,-1) = f(-1,-3)

    etc.

    So, what does f(2,y) = 2 + |y| tell you, when combined with f(x,y)=f(y,-x)?
     
  4. Oct 26, 2005 #3
    ok, that's what i thought after working with the problem for a bit. so is the answer "b" because you get a function of y?
     
    Last edited: Oct 26, 2005
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