Evaluate JF.dr from (0,0) to (9,3) along the curve y=vx if Ē(x, y, z) = x’yi...
Evaluate xy dx + (x + y)dy along the curve y = 3x? from (-2,12) to (1,3). с xy dx + (x + y)dy = 0 xy dx + с (Type an integer or a simplified fraction.)
X 16.2.23 Evaluate si xy dx + (x + y)dy along the curve y= 2x² from (-3,18) to (2,8). C { xy dx xy dx + (x + y)dy = С (Type an integer or a simplified fraction.) ts
Evaluate xy dx + (x+y)dy along the curve y=2x? from ( - 3,18) to (-2,8). с | xy dx +(x+y)dy = [ С (Type an integer or a simplified fraction.)
Evaluate SSJ (+y– 32) 2V where E = {(x, y, z)| - 55y<0,0 < x <y, 0 <z<x+y?}
3. Divergence Find the divergence of: a) Ē(x, y, z)=(-2y x 0] b) F(x,y,z)= (y2 – 2x 5x’y x+37] c) v =[3y–2yx xy? -62?x]
Given the function ry g(x, y) = g(x, y) lim (x,y)(0,0) a. Evaluate iii. Along the line y i. Along the x-axis: x: iv. Along y x2: ii. Along the y-axis: g(x, y) exist? If yes, find the limit. If no, explain why not. b. Does lim (r,y)(0,0) c. Is g continuous at (0,0)? Why or why not? d. The graphs below show the surface and contour plots of g (graphed using WolframAlpha). Explain how the graphs explain your answers...
3. Use Stokes' Theorem to evaluate [ſcurl Ē. d5 where F(x, y, z)= x?y?zi + sin(xyz)ị + xyzk, o is the portion of the cone y² = x² +z? that lies between the planes y=0) and y = 3, oriented in the direction of the positive y-axis. [2187 1/4]
5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3) 5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3)
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...
Evaluate the line integral of the function f(x,y)= (x+y2)/(sqrt(1+x2)) over the curve C: y=x^2/2 ; from (1,1/2) to (0,0)