F-dS where S is the cylinder x? +-2, 0 s y < 2 oriented by the unit normal 5- Let F(x,y,z)= (-6x,0,-62). Evaluate pointing out of the cylinder. 6-Let F(x, y,2)- yi- xj +zx°y?k. Evaluate (Vx F) . dS where S is the surface x2+y+32 - 1, z <0 oriented by the upward- pointing unit normal. F-dS where S is the cylinder x? +-2, 0 s y
Given the following vector field and oriented curve C, evaluate F.T ds. F = (-6y,6x) on the semicircle r(t) = (6 cost,6 sin t), for Ostst [F-T ds =D (Type an exact answer, using a as needed.)
Evaluate the following integral. + 6x - 1 dx X-X Find the partial fraction decomposition of the integrand. St*6x=1&x=SO dx Evaluate the indefinite integral. S*** + 6x - 1 3 X-X dx =
Solve the following system of equations by using the inverse of the coefficient matrix. 6x+5y=5 x +2y-2 a)○x=1, y=-1 b) Ox-1, y-1 c)/︵ x = 0, y=1 f) None of the above.
(3 points) Maximize the function P = 7x – 8y subject to x > y > 6x + 5y = ( 10x + 2y > ΛΙ ΛΙ V 0 0 30 20 What are the corner points of the feasible set? The maximum value is and it occurs at . Type "None" in the blanks provided if the maximum does not exist.
Compute the Riemann sum S for the double integral (6x + 5y) dA where R = [1,4] × [1, 3], for the grid and sample points shown in figure below S = 155 Compute the Riemann sum S for the double integral (6x + 5y) dA where R = [1,4] × [1, 3], for the grid and sample points shown in figure below S = 155
2. (2 pts) Determine the type of the critical point (0,0) for the system x' =-7x+ 5y, y' =-6x 4y. Sketch a phase portrait based on the eigenvectors, and the direction that the sign of the eigenvalue indicates. 2. (2 pts) Determine the type of the critical point (0,0) for the system x' =-7x+ 5y, y' =-6x 4y. Sketch a phase portrait based on the eigenvectors, and the direction that the sign of the eigenvalue indicates.
16.1 Evaluate [[cz + 3y – x²dS where S is the portion z = 2 – 3y + x2 that lies over the triangle in the xy-plane with vertices (0,0), (2,0), (2, -4).
Q3. x² +6x+8y + 25 = 0 * +6x= -84–25 (x+3)²-9=-84-95 (x+3) = -84 – 16 (x+3)= -8[y + water (-3,-2) faces (-3,-4) Axis of st. x=-3 Directx y zo 1233 Arab Academy for Science, Technology and Maritime Transport - Sharjah Branch No.5: F(x) = In 1 + x Solution: F(x)= In 1+x F(0) = ln 1 = 0 F(0)=1 F"(0)=-1 F"(0) = 2 F4(0) = -6 F'(x) =x = (1+x)" F"(x) =-(1+x)=2 F"(x) = 2(1+x)=3 F4(x) = -6(1+x)-4 F(x)=F(0)...
Problem 3 (8 marks) Evaluate the surface integral JJz"(x+y*)dS , where S s the part of the plane z 3 inside the paraboloid z = x2 + y2. Problem 3 (8 marks) Evaluate the surface integral JJz"(x+y*)dS , where S s the part of the plane z 3 inside the paraboloid z = x2 + y2.