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Taylor's formula for two variables

  1. Apr 29, 2013 #1
    http://sphotos-h.ak.fbcdn.net/hphotos-ak-ash4/485580_10200547582988715_854455727_n.jpg [Broken]

    In formula 1 it says F(1) = F(0)+F'(0)+ 0.5F''(C)
    Where the heck dos the C come from? I thought they were applying taylor's formula to find an approximation of F(1), around t=0. Then c=0, right? Is it because h and k are very small?

    In other words, how is there room for a c, when x=1 and x0=0?
    taylor%20series.png
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Apr 29, 2013 #2
    http://sphotos-a.ak.fbcdn.net/hphotos-ak-prn1/945518_10200547626669807_1364716261_n.jpg [Broken]

    At point 4, why is another test needed? Since the term (h*fxx+k*fxy)2 is always positive, then term Q(0) must always have the same sign as fxx, no?
     
    Last edited by a moderator: May 6, 2017
  4. Apr 29, 2013 #3
    I figured out the question in post 1, but I still don't understand the1 in post 2.
     
  5. Apr 29, 2013 #4

    HallsofIvy

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    No, it could be 0, as is pointed out in your insert.
     
    Last edited by a moderator: May 6, 2017
  6. Apr 29, 2013 #5
    oh,of course. thanks!
     
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