## Answers

3.0 F = <y-Z, 2-2, k.) inc. F (3,4, 2) = (1-2)i + (Z-x)) +(2-4) C: x² + y2 = 9 and 57. . y = 1 3=r + 0 21 0-0 to ari 21 32 -s (9-x) = -«) + (x+998) (eu vejrozh) a - s (y - 3)d + (7-4) 4y 12-y)<%. Conside e sine-17)(+33in.gdt) los 820 + (17-360) (364648) Y = 3 sing and z=7 de = -3 sinodo dy' 2360 Ode dz=0 - 2-asino +357 Sino 0.0 + 3 V7 63 0 - 9 Cy? B) do.

- 3-9 (Sm*6+cos +3-Fi ( simt + 1030)} do en f 44 3V1 (Simb + 4 0 )}dt 8-48 +387(+680 +Sino) - - 9. (2.) +351 (+ G 21+Sinan) - 35 footsine) - zis: 2x2=16" - - 180 +32(1+0) = 357 (-1+0) R. = - 18n. 2. JF.

Dx = -181, solo (6) By Stoke's theorem, XF). ñ ds and S x² + y ²7 2 216 :Z57 where e kty » +3=16 So, e is exactly same as previous ? *+y = 9 Now, axtli ja lis-s-a) tittet u²+ y = 16 1922- ung 21-22 -2 -20

5. (x² + 22 - 16) Ilh.al 18(uty 12-16) = 2x1+zyj +25 √4x²+4 4 4 47 fom B & 4n2+442 +422 row since this supface s has a projection on Z= i , their Spoxt).ndy 14 4 2 + 7 = 16 and 5 Troki so, Rus region sounded by a and = 7 = SS-28+ 23 +2²) . (2x + 2y3 +22²) audy Vynuyh+422 Dicepe 4x +49 +42 dudy 32 let na Cost y rosino z = 7 3 4(76038) + 4. (rSine) +47) dodel dudy - nonat s from oto & 020226 + o from a to 21 √4x²+ 4y? 422 23 - JS - 257 * Deo 920 -- S" (334 30 9242132€ 13.9 ]do = -√2 (18 coso + 18 sino + aft) do = -1/2 ( 18 Sime I 18 (oso +970) - Walk 12 sim 2n pr 18 6920 49 -2n) - (1859-1863040)] -- 10 -18 +18617) - (0-10)] 2 1 18 n t = - 181

SOS nas = - 18 n = gran (♡ Then surface given by S₂ is same as previous regiong R, which is projected in aſa.

.
So, SSG x² Jands = Sex Bondy = -181 Si ) i S (3x) r ds = s Fias-a18 Ty (By Stokes them 8 sen

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