Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

Sec. 12] Taylor's Formula for a Function of Several Variables_221
All subsequent derivatives are identically zero. Putting these results
into formula (2), we obtain:
~ 2
[/i -64-2/z k- 3-f fc
2
8 -
( 24)) + [/i G + ^y 3/z 2 2
fc. + 3/ife -0-f *'( 12)]
powers
1996. Expand f (x i ft, y + k) in a series of positive integral
of h and fe if
1997. Expand the function f (x, y) = * 2
+ 2xy + 3y*
2/y 4 by Taylor's formula in the neighbourhood of the point
(-2, 1).
1998. Find the increment received by the function f(x,y)~
^-x*y when passing from the values x=l, {/=! to
1999. Expand the function f(x, y, z) = Jc'-fy 1
+ 2* +2xy yz
4* 3# z-l-4 by Taylor's formula in the neighbourhood of
the point (1, 1, 1).
2000. Expand f (x t ft, //-J fr, z-| /) in a series of positive in-
tegral powers
of /?, k, and /, if
/ (x, y, z) =--= x 2
*
// 4 - z 2
2jr// 2A:e 2yz.
2001. Expand the following function in a Maclaurin's series
up to terms of the third order inclusive:
/(.Y, //) = ?* sin//.
2002. Expand the following function in a Maclaurin's series
up to terms of order four inclusive:
/ (x, //) = cos x cos y.
2003. Expand the the neighbourhood
following function in a Taylor's series in
of the inclusive:
point (1, 1) up to terms of order two
/(*. {/) = {/*
2004. Expand the following function in a
the neighbourhood
Taylor's series in
of the point (1, 1) up to terms of order
three inclusive:
6x