CCF20110118007

ozz uapowieazi ao znaan

12.39.    Funkcja jest ciągła dla (x,y) € IR².

12.40.    Funkcja jest ciągła dla (x, y) € IR².

Rozdział 13

13.4.    || = 3y + 2x, % = 3.x + 4y.

13.5.    || = 5x'¹ sin(xy) + x⁵ycos(xy), || = x⁶ cos(xy).

13.6.    || = cos(xy) — xy sin(xy), || = — x²sin(xy).

¹³-⁷- % ^{= 2t}8(* + 2/²) co_S2(i+2/2), §| = 4y tg(x + y²) ^2^2) •

13.8.    || = 2x(llx + 2y)(x + 2y)¹⁹, g = 40x²(x + 2y)¹⁹.

13.9.    Ęl = l <LL = ^xi~^xV²

13.10.    g = y² + I, g = 2xy.

13.11.    || = 3ye^3xy + |, g = 3.xc³^ + J.

13.12.    || = yx^y~^l, g = x^y lnx.

13.13.    = ^^+xey,    _xev+xe^y

cte    ’ a?/

13.14.    || = x^yx (y lnx + y), g = x^yx+1 lnx.

13.15.    || = 2xsin³(x²y²) + 6x³y²sin²(x²y²) cos(x²y²), g = 6x⁴y sin²(x²y²) cos(x²y²).

¹³¹⁶- & =    §£ = **. §{ = *v-

13-17. §r ^{== 3}(^a’² + 2/)i S ⁼ 3(y² + x), || = 3z².

13-18. % = W²-²³. g = ^2xyz³, g = 3xy²z².

13.19.    = sin(xy²z³) + xy²z³ cos(xy²z³), g = 2x²yz³ cos(xy²z³), g = 3x²y²z² cos(xy²z³).

13.20. || = x^y2_1 yz, g = x^y2zlnx, || = x^!/2ylnx.

13.21. || = x^y2_l y², g = x^yZ y^2-1 z lnx, || = X’*⁷² y² lnx lny.

13.22. || = y²z³t\ g = 2xyz³t⁴, §| = 3xy²z²t^Ą, §| = 4xy²z^zt^z.

13.23. g = l, g = 2y, g = 3z², g = 4i³.

13.24.    g = siny cos(zi), g = x cos y cos(zt), g = — ort siny sin(z/.), g = —xzsiny sin(zi).

13.25. a. .7/(1,2,3)

2 24 432

1 0 1

c. .//(I, —1)

4

3 -1

13.26. g = 2xy³ + 3y, g = 3x²y² + 3x, 0 = 2y³, 0 = 6x²y, 13.28. g = sin(xy) + xy cos(.xy), g = x² cos(.xy), 0 = 2y cos(,xy)

a²l

xy² sin(.xy), 0 = -.x³ sin(xy), gg = 2x cos(xy) - x²y sin(xy).

13.31. g = cos(yz), g =-xzsin(yz), g = -xysin(yz), 0    0,

dy

= -«sin(yz), gg = -ysin(yz), 0 = -xz²cos(yz),

a²

a_z,

g = — xyz cos(yz) - xsin(yz), 0 = -xy²cos(yz).

13.32. g = 3y + 7x⁶y², g = 3x + 2x⁷y, 0 = 42x⁵y²,

0 = ^2x7>    = ³ + 14x⁽⁾y, 0 - 210xV, 0 - 0, g0

&

dy^{7 M} ’ ciyl 7507 = 14x⁶

oxćy^z

13.33. g — 3x², g — 12y⁵, g — 21z⁶, 0 — 6x, 0 — 60y⁴, 0 = 126z⁵, gg = 0, gg = 0, gg = 0, 0 = 6, 0 = 240y \

0 — 630z⁴,

dz

JUL

a³/

dydx^    dzdx²

JiL = n =o.

~dzdy²

dxdz'²

o,

° „ — o -

dydz¹    ’ dzdydx

13.36.

ye'

i a/

i, S =

0 -    + ^xy)> Łk - °> mk ~ ⁰⁾ 0 ~ y³⁽‘^xy’

0 _ x²e^xy + g, 0 - Jr, g0 - e^xy{2y + xy²), g0

a?/

0,

40 == x²ye^xy + 2xe^xy, 40 = ₀₎

- °> afafc ~ °>    ⁰

13.38.    Tak.

13.39.    Tak.

13.40.    Tak.

13.41.    Nie.

13.42.    Tak.

13.43.    Tak.

13.44.    Tak.

13.45.    Tak.

13.46.    Tak.

13.47.    Tak.

13.48.    Tak.

13.49.    Tak.

13.50. Ta

13.51. Tu