please don't solve anything. by mistake this question
please don't solve anything. by mistake this question 1 Verify Cauchy's theorem for the closed path c consisting of three straight lines joining A (1+1), B (34 j3), C (-1 + β) where r(...
3. Consider the vector field--(z+92)--Idzy2 + 412zk. Calculate / E.dr from (0,0,0) to (1.1,1) along (a) r f2 [10 marks] 0,0,0) to (b) the path from (0,0,0) to (1) consisting of the straight lines fro (1,0,0), then to (1,1,0), and then to (1, 1, 1). [10 marks] 3. Consider the vector field--(z+92)--Idzy2 + 412zk. Calculate / E.dr from (0,0,0) to (1.1,1) along (a) r f2 [10 marks] 0,0,0) to (b) the path from (0,0,0) to (1) consisting of the straight...
q4 please thanks (1) Let A - (0,0), B- (1,1) and consider the veetor field f(r, y,z)vi+aj. Evaluate the line integral J f.dr )along the parabola y from A to B and (i)along the straight line from A to B. Is the vector field f conservative? (2) For the vector feld f # 22(r1+ gd) + (x2 + y2)k use the definition of line integral to (3) You are given that the vector field f in Q2 is conservative. Find...
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'cos x)i +(e'sinx)j [Hint: Test F for conservative (c). Use green theorem to express the line integral as a double integral and then evaluate. where C is the circle x+y-4 with counterclockwise orientation. (d(Bonus10 pts) Consider the vector field Foxyz) a. Find curl F y, ,z> F.dr where C is the curve...