(1 point) Use the catalog of surfaces in your textbook to identify the surfaces given below....
(Quadric surfaces) Use the quadric surfaces handout on Canvas to answer the following. Do not use a graphing utility for this problem. i. Give the name of each of the surfaces below. ii. Identify the shape of the horizontal traces (parallel to the ry-plane). (Hint: these surfaces may be oriented differently than on the handout - for example, the equation -y = 2x² +522 describes an elliptic paraboloid that opens' along the negative y-axis, and the horizontal traces are parabolas.]...
Use polar coordinates to find the volume of the given solid. Below the paraboloid z = 12 - 3x2 - 3y2 and above the xy-plane Step 1 We know that volume is found by V = flr, e) da. Since we wish to find the volume beneath the paraboloid z = 12 - 3x2 - 3y2, then we must convert this function to polar coordinates. We get sles z = f(r, 0) = - 31 We also know that in...
Cuenticn Hel Which of the given quadratic surfaces can be generated by revolving a curve in one of the coordinate planes about a coordinate axis, assuming a b c0h Hyperboloid of bwo sheets Hyperbolic paraboloid Hyperboloid of one sheet paraboloid cipsoid Select all that apply Hypertoloid of hwo sheets A Hyperboloid of one sheet C. Eliptic paraboloid DE Elipsold D. Hyperbolc peraboloid None of those Click to select your answeris) and then click Check Answer Clenr All All parts showing...
3. a) (12,5 point) What is the definitions of cone and cylinder surfaces. Write the vectoral and parametric equations of them with their figures. b) (12,5 point) Identify and construct the surface whose equation is ra+yz = 0. Cone or cylinder surface.
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...
Consider the surface whose equation is z = -2(y+1)^2 + (x+1)^2 - 1 i) determine a surface of the form (*) whose graph you can translate, rotate, or reflect to obtain the graph of the given surface. Provide the steps one would follow to manipulate the graph of your surface to get the graph of the given surface. Form could be Ellipsoid, Cone, Elliptic Paraboloid, Hyperboloid of One sheet, Hyperbolic paraboloid, and Hyperboloid of two sheets.
1 point) Match the functions below with their level surfaces at height 3 in the table at the right. 1. f(x,y,z) 22 3x 2.f(x,y,z) 2y +3x 3. f(x, y,z) 2y +3z -2 (You can drag the images to rotate them.) Enable Java to make this image Enable Java to make this image interactive] Enable Java to make this image Enable Java to make this image Enable Java to make this image Enable Java to make this image interactive] 1 point)...
Evaluate the surface integral F dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For dlosed surfaces, use the positive (outward) orientation F(x, y, 2) _ yj-zk, sconsists ofthe paraboloid γ_x2 +22, O sys1, and the disk x2 +22 s 1.7-1. Need Help? to Tter Evaluate the surface integral F dS for the given vector field F and the oriented surface S. In other words, find the...
3. Let f be the continuously different iable function f(r.v)- if (x.y)-(0.0) otherwise (a) Use the limit definition to caleulate both partial derivatives of f at (x.y)-(0,0) (b) Find f(z, y) and f,(z,y) for (r,y) (0,0). (0.0) (c) Use the limit definition of the partinl derivative to calculate (0,0) and (d) Find the tangent plane of the hyperbolic paraboloid z f(z,y)-- From the tangent plane, describe if this hyperbolic paraboloid is trending up or down when moving from point A(1,-2,0)...
Please do #2 40 1. 16 pts) Evaluate the integral( quadrant enclosed by the cirle x + y2-9 and the lines y - 0 and y (3x-)dA by changing to polar coordinates, where R is the region in the first 3x. Sketch the region. 2. [6 pts) Find the volume below the cone z = 3、x2 + y2 and above the disk r-3 cos θ. your first attempt you might get zero. Think about why and then tweak your integral....