2xzfy2xyz2fz2yzx2fxx2zfxz2xfyz2z
fxx0012fxz1022fyz0100
t
t
t
t
4
zx
2si
2x
2zt
si
2x2zxt
2cos2x2ztt
cos2x2
t
t
2ztt
zxt

2cos2x
2cos2x2
2

0
51
zx

yx2
y
ex
zy

1
e
yx

dz

x

yx2
y
exdx
1
e
yx
dy

x
2
z

1l
x22

y2zx

x2
x
y2
zy

x2
y
y2
dz

x2
x
y2
dx
x2
y
y2
dy
y

3zx
x21y2

x2
yy2
x
1

zy
x1y2
xx2y2
x
ydxxdy
dz

x2y2
4uxyzxyz1uyzxyzl
xuzyxyzl
x
duyzxyz1dxzxyzl
xdyyxyzl
xdz
6设对角线为z则z
x2y2zx
xx2y2
zy

y
xdxydy
dz
x2y2
x2y2
当x6y8x005y01时zdz6005801005m6282
7设两腰分别为x、y斜边为z则zx2y2
zx
xx2y2
，zy

y
xdxydy
dz

x2y2
x2y2
设x、y、z的绝对误差分别为x、y、z
f当x7y24xx01yy01时z7224225
zdz701240172242
0124z的绝对误差z0124
z的相对误差z01240496z25
8设内半径为r，内高为h，容积为V，则
Vr2hVr2rhVhr2dV2rhdrr2dh
当r4h20r01h01时
VdV231442001314420155264cm3
习题13
1duf
dxf
dyf
dz
yz
x
xy
zaeax
z22aax1
dxxdxydxzdx1xy21xy2
1xy2
z
z
z
yzaxz2axyax1ax1eax1a2x2



z2x2y2
ax14x2e2ax
2zf
f



x
arcsi
4x3
xxx121x2y2
x4y4
4x3arcsi
1x2y2
xl
x4y4

x4y4
1x2y2x2y2
zf
f



y
arcsi
4y3
yyy121x2y2
x4y4
4y3arcsi
1x2y2
yl
x4y4


x4y4
1x2y2x2y2
3
1
ux

2xf1

ye
xy
f2

uy


2yf1

xexy
f2

2
ux

1y

f1
uy

xy2

f1
1z
f
2

uz

yz2

f2
3
ux

f1

yf2

yzf3
uy

xf2

xzf3

uz

xyf3

fu
u
u
4x2xf1yf2f3y2yf1xf2f3zf3
4
1
zx

yf1
zy

xf1

f2

2zx2

y2
f11
2zxy

f1

yxf11

f12

f1
xyf11

yf12
2zy2

xxf11

f12xf21

f22x2
f11
2xf12

f22
2
zx

y2
f1

2xyf2
zy

2xyf1

x2
f2

2zx2

y2y2
f11
2xyf122yf2
2xyy2
f21
2xyf22
2yf2y4f114xy3f124x2y2f22
2zxy

2yf1

y22xyf11

x2
f12

2xf2

2xy2xyf21

x2
f22

2yf12xf22xy3f112x3yf225x2y2f12
2zy2

2xf1
2xy2xyf11

x2
f12
x22xyf21

x2
f22
2xf14x2y2f114x3yf12x4f22
5uuxuy1u3uuuxuy3u1usxsys2x2ytxtyt2x2y
u21u23uu3u2u23u23r