Question

Q4: Fill in the blanks in the following: a. The first order partial derivatives Fulu, v) of the function (F(u, v)= u'sin(u+v+) equal b. The second order partial derivatives Fxx{x,y) of the function (F(x,y) =x’y-In (x²-y)) equal C. The tree diagram of the Chain Rule for the given function w=w(x,y),x=x( P.4.5), y=y(p,u,v), s=s(u,v)pap(t) will be ........... d. The result of Cross Product Dot Product is a... and the result of Dot Product a is a e. The projection of vector Yon to vector X can be defined by the formula....... (16M) Q5: Choose then write the correct answer from the options given: 1. If A, B, C are vectors the result of (AX(B+C)] is equal : a. (AXB) + (AXC) b. A.(B+C) C. -LAX(B+Cj 2.Green's Theorem used on closed curve to convert the: a. Double Integral to Triple Integral. b. Line Integral to Double Integral. c. Double Integral to Line Integral. 3. If Ā B =0 then the vectors A and B will be : a. Zero vector. b. Parallel. c. Orthogonal. d. Unit vector. 4. The general solution of the nonhomogeneous second order differential equation consist from: a. One solution b. Tow solution c. Three solution. (16MI

Answer 1

Fruva u sincutvu) ) JE (gy): * ยV+ = 24 sincurv) + u.cos curv”) 4 งบ น 3 น here - constant t, PP u cos curo). 2v =2uv Coscutv) dr Chere 'u' constant) 6) xs) - - An (1) 2 x . P 28 ช zły " dar น. - 21 - (1-5) - 21 22 [): หอย 7 : - - - *** (ซ” ” (1” ฯ)” 21 -2 423 : - (1-3)”

c ) w :(Y,y) 2 = *CP,95), Y- YCP,U,V, S:14, v) P-plt). E 2 a 2 بلد u V t 20 2x ap ap dt + Jo ay op Jy Jp J 11 dx dt 316 31 مد 20 17 de sq aq aa de Jw dx.ds ax os au + dw dy sy du DEL w OLO dz, ƏS dx as ar + do dy ay Jw дү ģa Nector. of d) The result the result of aga Salar (scalar) cross product Dot producto Dot product ao vector on vector e) projection g (9.x) 181 5) 1) AX (B+C) =) ĂX B + AX 2) Green's theorom line integral to double integral 3) Āx B = 0-)ABSINO = 0 =) Sino = 0 %) 0 =0 ; So parallel 4) one solution