MINl Review Problems for CH. 1, 2 and 3 Q) Describe the following surfaces with a...
2.31 solution Section 2.5-Constant-Coordinate Surfaces 2.31 Describe the intersection of the following surfaces: (a) * = 2, y = 5 (b) x = 2, y = -1, z = 10 (c) r = 10, 0 = 30° (d) p = 5, 6 = 40° (e) $ = 60°, z = 10 (f) r = 5, 0 = 90°
Q4. Describe the intersection of the following surfaces a) p = 3, and 3, and the surface 90° SO = 135°, 90° 5o = 180°, r = 5. b) y = 1 and the surface, r = 3. c) -2 5 x,y s 2,2 = 2 and the surface, 0 = 90°. d) 0 = 45° and the surface , Q = 270º.
Parameterize the following surfaces in R3. Describe if the surface is open or closed. If the surface is open, give a parameterization of its boundary, 6. Parametrize the following surfaces in R3. Describe if the surface is open or closed. If the surface is open, give a parametrization of its boundary (positively oriented). (a) The part of the plane z - 2y 3 inside the cylinder 2 y16 (b) The sphere of radiuscentered at the origin. (c) The part of...
Please could you answer 3. Question please clearly write Q3. For a closed surface defined by the surfaces 3,p-5, ф z = 5, Calculate, by writing the respective integrations, 100. ф 130, z 3, and (a) The volume enclosed by the given surfaces (b) The total area of the enclosing surface (c) The total length of the twelve edges of the surfaces (d) The length of the longest straight line that lies entirely within the volume (a) Verify divergence theorem...
Please do both of the problems! Thank you ! [4 pts] Problem 2. Verify that is a solution of the partial differential equation Uzr+ Uyy = 5 ptsl Problem 3. (a) Verify that |T, — т 21-Z Y2 y 22 - z= 0 Уз — у 23 — 2 Тз — Т is an equation for the plane through the three noncollinear points P(x1, yi, z1), Q(x2, V2, 2),R(x3, ^3, Z3) (b) Use vectors to verify that the distance from...
question #6 1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1 (d) r2+y-22+1 0 (e) -y2+-1 0. 2. Find an equation for the surface consisting of all points that are- point (1,-3, 5) and the plane r = 3. 3. Sketch the curve F(t)<t cos(t), t sin (t), t > 4. Find a vector equation that represents the curve of the intersec r2y =9 and the plane y + z = 2. 5. Find a...
Q4 only: Question 3. Consider the region of R3 given by V is bounded by three surfaces. Si is a disc of radius 1 in the plane z -0. S3 is a disc of radius 2 in the plane z 3 and a) Make a clear sketch of V. (Hint: You could consider the cross-section of S2 with y-0, and then use the circular symmetry. (b) Express V in cylindrical coordinates. (c) Calculate the volume of V, working in cylindrical...
log(2 - 2) (x2 y Question 2. Consider the function f(x, y, (a) What is the maximal domain of f? (Write your answer in set notation.) (b) Find ▽f. (c) Find the tangent hyperplnes Te2)(r, y,z) and Tao2-)f(x, y, z). Find the intersection of these two hyperplanes, and very briefly describe the intersection in words (0,1, 1) and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2, 2, 1) is (d) On...
Answer each of the following question about the given the 3-dimensional surfaces x + y² +22 = 20 and 2 = x² + y². (2 pt) A) What quadric surfaces are represented by these equations? Give any details you can. x² + y2 + z = 20 := x2 + y2 (2 pt) B Make a sketch, nothing fancy just a sketch, of these surfaces and identify the space curve of intersection and describe this space curve in your own...
Could you please 1.question ЕЕ211 Electromagnetic Field Theory 1 Homework 2 Due by 12th of Nov, 2018 at 5 PM ANTALYA BILIM UNIVERSITY Homework 2 Q1. Given three vectors A, B, and C A-a +2a, -3a, Find (a) unit vector along A. (b) IA -BI (c) A.B (d) the angle between vectors A and B (e) The vector component of A in the direction of C. (f) AxC (g) A. (x C) and (A x B).C (h) (A x B)...