Let 8yx9 F(x, y, z)(9x8 In(4y2 + 10) + 6z7)i 3г) ј + (42x26 + Зу - 7sin zez) k ( + + 4y210 k,0 sts 1 (3+1)i (22)j and l...
4. Evaluate (F•dr for F(x, y, z)=(3xz)i +(2z - y)j+(22)k and с C:r(t)= (2t+1)i+(3).j+(5t)k, Ostsi
1. (25 pts] Let F(x, y, z) = (2xy4 +25)i + (4.x²y3 + 2yz3)j + (5x24 + 3y2 -2)k and let C be the curve given parametrically by r(t) = (3t+1)i + t?j + 5tk for 0 <t<1. Evaluate the line integral [F F. dr
2. (a) Let i. Show that F is cnservative in R i. Let C denote the path 1+cost,2+sint,3), 0StS 4 Evaluate F. dr Justify your answer. iii. Find a function y: R3-+ R such that F iv. Evaluate F.dr where「is the path y =r', z = 0, from (0.0.0) to (2.8.0) followed by the line segment from (2,8,0) to (1,1,2) 22 marks) 2. (a) Let i. Show that F is cnservative in R i. Let C denote the path 1+cost,2+sint,3),...
1. (25 pts] Let F(x, y, z) = (2xy+ + 25)i + (4x²y3 + 2yz3)j + (5x24 + 3y2z2)k and let C be the curve given parametrically by r(t) = (3t+1)i + tºj + 5tk for 0 <t<1. Evaluate the line integral Sa Spa
[25 pts] Let F(x, y, z) = (2xy4 + 25)i + (4x´y3 + 2yz3)j + (5x24 + 3y2-2)k and let C be the curve given parametrically by r(t) = (3t+1)i + t?j + 5tk for 0 <t< 1. Evaluate the line integral F. dr
(I point) Let F=21+(z + y) j + (z _ y + z) k. (1+4t). y = 4 + 2t, z = _ (1+t). Let the line l be x =- (a) Find a point P-(zo, 30, zo) where F is parallel to 1. Find a point Q (which F and I are perpendicular. Q= and l are perpendicular Give an equation for the set of all points at which F and l are perpendicular. equation: (I point) Let F=21+(z...
Let C be the curve (x - 3)2 + 9(y – 1)2 = 36, x +2y + z = 4, oriented counterclockwise when viewed from high on the z-axis. Let F be as shown below. Evaluate $.F. F.dr. F= (32² + 3y² + sin x? )i + (6xy + 3z)j + (x2 + 2yz)k $. F. dr= (Type an exact answer.) с
15.8 a. Use Stokes' Theorem to evaluate fF.dr where F(x,y,z) = (32-2y)i + (4x – 3y)j + (z +2y)k and C is the boundary of the triangle joining the points (1, 0, 0), (0, 1, 0), and (0, 0, 1). b. Find F.dr where F = 2zi - xj + 3y2k and S is the portion of the plane 3x + 3y + 2z = 6 in the first octant and C is its boundary.
1, Evaluate Jsx2ds where s is the portion of the cylinder 22ヤU-9 lying between z-1 and 22. 2. Let F(, y, z)i+ j + zk. Use the divergence thecrem to compute s F.ds where S is the portion of the cylinder x2 +y2-4 lying between z 1 and-2. 1, Evaluate Jsx2ds where s is the portion of the cylinder 22ヤU-9 lying between z-1 and 22. 2. Let F(, y, z)i+ j + zk. Use the divergence thecrem to compute s...
Please explain all steps. Thanks! 1. (25 pts) Let F(x, y, z) = (2xy + 25)i + (4.r?y3 + 2yz?)j + (5.624 + 3y222)k and let C be the curve given parametrically by r(t) = (3t+1)i + tºj + 5tk for 0 <t<1. Evaluate the line integral (Fd