os the come the graphic in spece r-r-2-1 tne corvect me l-Tdentify 4 25 4a s Deente the surface vepresentea by e cso...
10. Stokes' Theorem and Surface Integrals of Vector Fields a. Stokes' Theorem: F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sketch of curve C in the xy-plane. Let F(x,y,z) = <2z, x, y?». Compute the curl (F) c. d. Find a parametrization of the surface S: G(u,v)- Compute N(u,v) e. Use Stokes' Theorem to computec F dr
10. Stokes' Theorem and Surface Integrals...
10. Stokes Theorem and Surface Integrals of Vector Fields a Stokes Theorem:J F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sketch of curve C in the xy-plane. Let F(x,y,z) = <2z, x, y, Compute the curl (F) c. d. Find a parametrization of the surface S: G(u,v)ーーーーーーーーーーーーー Compute N(u,v) e. Use Stokes' Theorem to compute Jc F dr
10. Stokes Theorem and Surface...
7. Find the volume of the solid region that lies under the surface 2 = ry and over the region in the xy plane bounded by the curves y = 2r and y = r A. 4/3 B. 8 C. 8/3 D. 32/3 E. none of the above 8. Evaluate SSSE Vx2 + y2 dV where E is the region bounded by the paraboloid z = x2 + y2 and the plane z = 4. A. 87 B. 327 c....
QUESTION 5 Let the surface S be the portion of the cylinder x2 + y2 4 under z 3 and above the xy-plane Write the parametric representation r(z,0) for the cylinder x2 +y2 4 in term of z (a) and 0 (2 marks) Based on (a), find the magnitude of llr, x rell for the given cylinder (b) (6 marks) 1 1+ (e) Evaluate z dS for the given S (8 marks) Hence, use the divergence theorem to evaluate f,...
Problem 4 Let S denote the surface in R3 defined by z-(y2 + x2)-2, 1-г oo, and E be the region bounded by S and z -1. Show that you can fill E with paint but you cannot paint its surface. [10 marks]
Problem 4 Let S denote the surface in R3 defined by z-(y2 + x2)-2, 1-г oo, and E be the region bounded by S and z -1. Show that you can fill E with paint but you...
TR! MR FC vel TC MC ATC Profit S-6 $25 21 5 4 3 2 $25 $20 $153 $10 41 S33 Complete the table above, using the given information. a. Use the demand and supply schedules to plot both curves on a well-labeled graph. b. Now assume a price floor of $20 and indicate this on the graph. C. Calculate the value of the new consumer surplus, the value of the new producer surplus, and the value of the new...
a) Draw helical wheels for each of the following two sequences. 1) E-L-K-D-L-S-K-S 2) L-R-K-L-E-R-S-L b. In the diagram above show likely interactions between each sequence. C What is the name of the secondary structure this may form
Question 2 (1 point) Identify the surface r = 1, in cylindrical coordinates. Plane Cone Half plane Disc Sphere Circle Line segment Cylinder Use spherical coordinates to find the volume of the solid that lies above the cone z = V3x2 + 3y2 and below the sphere x2 + y2 + 2? first octant. Write = 1 in the V = L*S*%' * sin ødpdepdo 1. O 2. 1 d = < 3. À b= 4. 7T 2 5. Ő...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
In R3 minus the z-axis, consider the vector field 2(e) = (n Typ me i my2 +1) and the surfaces S: 5<2? + y2 <9, z = 0, S2 : 2? + y = 5, 05:52, Sz: 22 + y2 + x2 =9, 05:52 (a) Calculate Vov. [4 marks] (b) Show that Si U SUS3 is a closed surface. [4 marks] (c) Calculate the volume of the region R that is enclosed by SUS, US3- Hint: use cylindrical coordinates. [6...