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1. Find (2x2 + y2) DV where Q = { (x,y,z) 0 < x <3, -2 <y <1, 152<2} ЛАЛ
F(x, y, z) =< P, Q, R >=<-y +z,x-z,x-y> S: z = 9 - x2 - y2 and z>0 (9a) Evaluate W= $ P dx + Qdy + Rdz с
Q #1 (2 marks) Find the general solution for the DExy'-ymx1y, x>0, y>0.
(9) Stokes' Theorem for Work in Space F(x, y, z) =< P,Q,R >=<-y+z, x - 2,x - y > S:z = 4 - x2 - y2 and z>0 (9a) Evaluate W= $ Pdx + Qdy + Rdz с (9) Stokes' Theorem for Work in Space F(x, y, z) =< P,Q,R>=<-y+z, x - 2, x - y > S:z = 4 - x2 - y2 and z 20 (9b) Verify Stokes' Theorem.
homogeneous solution for n>-0, a) y[n] + 1.3y(n-1] + 0.4y[n-2] 0; y[-1-0, y[-2] 5 yn]- 1
1. Find (2.rº + y) DV where Q = { (z,y,z) | 0<<<3, -2<y<1, 1<2<2} 1 / 12
>> x = 0; y = 1 >> while y < 40 x = x + 1; y = y + 2^x; end >> disp(x), disp(y) 4. >> f = @ (x, y, z) sqrt ((x + y)/z); >> f(6, 12, 2) >> f(20, 16, 1) 5. >> A = [1 2; 1 -2]; >> B = [3; 5]; >> D = det(A) >> C = inv(A) * B
9. Let x,y > 0 be real numbers and q, r E Q. Prove the following: (а) 29 > 0. 2"а" and (29)" (b) x7+r (с) г а — 1/29. 0, then x> y if and only if r4 > y (d) If q (e) For 1, r4 > x" if and only if q > r. For x < 1, x4 > x* if and only if q < r.
(10) 2. Solve the homogeneous equation by making the substitution y = xv y' x + 2y 2x + y' > 0.
(8) The Divergence Theorem for Flux in Space F(x, y, z) =< P, Q, R >=< xz, yz, 222 > S: Bounded by z = 4 – x² - y2 and z = 0 Flux =S} F înds S (8a) Find the Flux of the vector field F through this closed surface. (8) The Divergence Theorem for Flux in Space F(x,y,z) =< P,Q,R >=< xz, yz, 222 > S: Bounded by z = 4 – x2 - y2 and z...