8. (10 pts) Find following surface integrals: S: (u, v) = ui + vj+uK, O SUS...
10. Consider the surface S parameterized by w r= (cos y, sin v, u + sin v), -3 <u <3, 050 < 27 *** (a) Write a linear equation for the tangent plane to the surface at (0,1,1) (b) Compute the surface area of S.
12. Given that F(x,y,z) = 6x?i + 1829 + 36x?yk and that S is the surface 7(u, v) = ui + 2vſ + Zuvk where 0 su s 1 and 0 sv<2, compute the flux •ds of the vector field † through the surface S oriented in the upward direction. (4 points)
Question 1 1 pts Let F= (2,0, y) and let S be the oriented surface parameterized by G(u, v) = (u? – v, u, v2) for 0 <u < 12, -1 <u< 4. Calculate | [F. ds. (enter an integer) Question 2 1 pts Calculate (F.ds for the oriented surface F=(y,z,«), plane 6x – 7y+z=1,0 < x <1,0 Sysi, with an upward pointing normal. (enter an integer) Question 3 1 pts Calc F. ds for the oriented surface F =...
(10 pts) Suppose an object moves along a line with velocity v(t) = 3+- 18t +24, for 0 st < 5, where t is measured in seconds and velocity have unit of ft/s. (a) Determine when the motion is in the positive direction and when it is in the negative direction. (b) Find the displacement of the object on the interval 0 st 35. (c) Write down an expression for the distance traveled by the object over the interval 0...
10. The surface described by r(u, v) = cosu i + sinu cosv j + sinu sinv k where 0 <u<r and 0 < < 2n is a a. Cone b. Cylinder c. Sphere d. Upper half of an ellipsoid e. Upper half of a sphere f. None of these 11. The surface described by r(u, v) = 3cosu cosv i + 2sinu cosv j + 6siny k where 0 <u<2n and 0 <vn/2 is a a. Cone b. Cylinder...
3. (3 points) Let the surface S be parametrized by r(u, v) = (bcos u, sin u, v) for (u, v) E D where D = {(u, v) O SUST, SU <3}. Set up the iterated integral, but do not evaluate, the surface area JJsdS (I want the iterated integral for du du, and in that order. Do not even try to evaluate this integral!).
1. Who's that surface? Consider the function Flu, y) = (v cosu, v sin u, u), 0 Su<27, -2 SU <2. The goal of this problem is to figure out what surface this function parametrizes! (a) Find a parametrization of the coordinate curve with u held constant as u = u. Plot a couple of these curves in 3D to see what they look like. (b) Find a parametrization of the coordinate curve with v held constant as v =...
Question 26 1 pts Use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the given integral. Let F = < yz, xz, xy). Find the work done by this force field on an object moving from (1,1,1) to (4,4,4). O 54 57 60 o oo 63
1. u Test s. = <1,2,2>. Point p (-1,0,2). Find (1), the direction cosines of u 12. the live through point p that's perpendicular to ū and parallel to the place 2x-y +38=7 2. Name and sketch the graph for the equation 4x²+y²-28 -8x + 2y +8=0.
8. Solve V?u=0, 2<r<4,0<O<21, (u(2,0) = sin 0, u(4,0) = cos 0,0 5 0 5 21.