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Multivariable sketch

  1. Jan 20, 2006 #1
    Here is the problem i'm having some trouble with. The answer is fairly simple, it is the power of the e function. (the parabola x = y^2 + 1) i'm not sure how to get that, i could use some hints/help, thanks!
    [​IMG]
     
  2. jcsd
  3. Jan 20, 2006 #2

    StatusX

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    Think about what values for the power of an exponent give a result greater than one.
     
  4. Jan 21, 2006 #3

    HallsofIvy

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    Are you aware that "The answer is fairly simple, it is the power of the e function. (the parabola x = y^2 + 1)" is NOT precisely true? That is, the region you are asked to sketch is NOT the parabola itself. The parabola is a boundary of the region. Indeed if you think about the fact that "power of the e function" is NOT x= y^2+ 1 nor a parabola, you might see what StatusX means!
     
  5. Jan 21, 2006 #4

    benorin

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    I'll be kind: recall that [tex]e^w \geq 1[/tex] if, and only if, [tex]w\geq 0,[/tex] that is, if, and only if the exponent of e is greater than or equal to 0. You are asked to find (and sketch) all points in xy-plane (e.g. all values of x and y) such that [tex]e^{1-x+y^{2}}\geq 1,[/tex] which occurs if, and only if, [tex]1-x+y^{2}\geq 0[/tex] which describes the region in the xy-plane bounded by (and to the left of) the parabola [tex]x=1+y^{2}[/tex].
     
  6. Jan 21, 2006 #5
    ohh, i see, i forgot that to get thats how to get the entire function greater than 1, i get it now, thanks everyone!
     
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