Taylor's formula for two variables

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Discussion Overview

The discussion revolves around the application of Taylor's formula for functions of two variables, specifically addressing the presence of a constant 'C' in the formula and the implications of certain terms in the context of mathematical tests related to the formula.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the origin of the constant 'C' in the Taylor's formula, suggesting that it should be zero when approximating F(1) around t=0, and wonders if the presence of 'C' is due to the smallness of variables h and k.
  • Another participant seeks clarification on a specific term in the formula, questioning the necessity of an additional test when a certain term is always positive, suggesting that it should maintain the same sign as fxx.
  • A later reply indicates that the term could be zero, challenging the assumption made in the previous post regarding the sign of Q(0).

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the Taylor's formula and the necessity of additional tests, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

There are unresolved assumptions regarding the conditions under which the Taylor's formula is applied, particularly concerning the values of h and k, as well as the implications of the terms discussed.

Nikitin
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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
 
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http://sphotos-a.ak.fbcdn.net/hphotos-ak-prn1/945518_10200547626669807_1364716261_n.jpg

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?
 
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I figured out the question in post 1, but I still don't understand the1 in post 2.
 
Nikitin said:
http://sphotos-a.ak.fbcdn.net/hphotos-ak-prn1/945518_10200547626669807_1364716261_n.jpg

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?
No, it could be 0, as is pointed out in your insert.
 
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oh,of course. thanks!
 

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