# Taylor's formula for two variables

1. Apr 29, 2013

### Nikitin

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?

Last edited by a moderator: May 6, 2017
2. Apr 29, 2013

### Nikitin

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
3. Apr 29, 2013

### Nikitin

I figured out the question in post 1, but I still don't understand the1 in post 2.

4. Apr 29, 2013

### HallsofIvy

Staff Emeritus
No, it could be 0, as is pointed out in your insert.

Last edited by a moderator: May 6, 2017
5. Apr 29, 2013

### Nikitin

oh,of course. thanks!