Problem 1QC: Describe the surface r(u, v) = 2cosu,2sinu,v,for 0 u and 0 v 1. Problem 2QC: Describe the surface r(u, v) = vcosu,vsinu,v, for 0 u and 0 v 10. Problem 3QC: Describe the surface r(u, v) = 4sinucosv,4sinusinv,4cosu, for 0 u /2 and 0 v . Problem 4QC Problem 5QC: Explain why explicit description for a cylinder x2 + y2 = a2 cannot be used for a surface integral... Problem 6QC: Explain why the upward flux for the radial field in Example 8 is greater for the hemisphere than for... Problem 1E: Give a parametric description for a cylinder with radius a and height h, including the intervals for... Problem 2E Problem 3E: Give a parametric description for a sphere with radius a, including the intervals for the... Problem 4E Problem 5E: Explain how to compute the surface integral of a scalar-valued function f over a sphere using a... Problem 6E: Explain what it means for a surface to be orientable. Problem 7E: Describe the usual orientation of a closed surface such as a sphere. Problem 8E: Why is the upward flux of a vertical vector field F = 0, 0, 1 across a surface equal to the area of... Problem 9E: Parametric descriptions Give a parametric description of the form r(u,v)=x(u,v),y(u,v),z(u,v) for... Problem 10E: Parametric descriptions Give a parametric description of the form r(u,v)=x(u,v),y(u,v),z(u,v) for... Problem 11E: Parametric descriptions Give a parametric description of the form r(u,v)=x(u,v),y(u,v),z(u,v) for... Problem 12E: Parametric descriptions Give a parametric description of the form r(u,v)=x(u,v),y(u,v),z(u,v) for... Problem 13E: Parametric descriptions Give a parametric description of the form r(u,v)=x(u,v),y(u,v),z(u,v) for... Problem 14E: Parametric descriptions Give a parametric description of the form r(u,v)=x(u,v),y(u,v),z(u,v) for... Problem 15E: Identify the surface Describe the surface with the given parametric representation.... Problem 16E: Identify the surface Describe the surface with the given parametric representation.... Problem 17E: Identify the surface Describe the surface with the given parametric representation.... Problem 18E: Identify the surface Describe the surface with the given parametric representation.... Problem 19E: Surface area using a parametric description Find the area of the following surfaces using a... Problem 20E: Surface area using a parametric description Find the area of the following surfaces using a... Problem 21E: Surface area using a parametric description Find the area of the following surfaces using a... Problem 22E: Surface area using a parametric description Find the area of the following surfaces using a... Problem 23E: Surface area using a parametric description Find the area of the following surfaces using a... Problem 24E: Surface area using a parametric description Find the area of the following surfaces using a... Problem 25E: Surface integrals using a parametric description Evaluate the surface integral Sf(x,y,z)dS using a... Problem 26E: Surface integrals using a parametric description Evaluate the surface integral Sf(x,y,z)dS using a... Problem 27E: Surface integrals using a parametric description Evaluate the surface integral Sf(x,y,z)dS using a... Problem 28E: Surface integrals using a parametric description Evaluate the surface integral Sf(x,y,z)dS using a... Problem 29E: Surface area using an explicit description Find the area of the following surfaces using an explicit... Problem 30E: Surface area using an explicit description Find the area of the following surfaces using an explicit... Problem 31E: Surface area using an explicit description Find the area of the following surfaces using an explicit... Problem 32E: Surface area using an explicit description Find the area of the following surfaces using an explicit... Problem 33E: Surface area using an explicit description Find the area of the following surfaces using an explicit... Problem 34E: Surface area using an explicit description Find the area of the following surfaces using an explicit... Problem 35E: Surface integrals using an explicit description Evaluate the surface integral Sf(x,y,z)dS using an... Problem 36E: Surface integrals using an explicit description Evaluate the surface integralSf(x,y,z)dSusing an... Problem 37E: Surface integrals using an explicit description Evaluate the surface integral Sf(x,y,z)dS using an... Problem 38E: Surface integrals using an explicit description Evaluate the surface integral Sf(x,y,z)dS using an... Problem 39E: Average Values 39. Find the average temperature on that part of the plane 2x + 2y + z = 4 over the... Problem 40E: Average values 40.Find the average squared distance between the origin and the points on the... Problem 41E: Average values 41.Find the average value of the function f(x, y, z) = xyz on the unit sphere in the... Problem 42E: Average values 42.Find the average value of the temperature function T(x,y,z)=10025z on the cone... Problem 43E: Surface integrals of vector fields Find the flux of the following vector fields across the given... Problem 44E: Surface integrals of vector fields Find the flux of the following vector fields across the given... Problem 45E: Surface integrals of vector fields Find the flux of the following vector fields across the given... Problem 46E: Surface integrals of vector fields Find the flux of the following vector fields across the given... Problem 47E: Surface integrals of vector fields Find the flux of the following vector fields across the given... Problem 48E: Surface integrals of vector fields Find the flux of the following vector fields across the given... Problem 49E: Explain why or why not Determine whether the following statements are true and give an explanation... Problem 50E: Miscellaneous surface integrals Evaluate the following integrals using the method of your choice.... Problem 51E: Miscellaneous surface integrals Evaluate the following integrals using the method of your choice.... Problem 52E: Miscellaneous surface integrals Evaluate the following integrals using the method of your choice.... Problem 53E: Miscellaneous surface integrals Evaluate the following integrals using the method of your choice.... Problem 54E: Cone and sphere The cone z2 = x2 + y2 for z 0, cuts the sphere x2 + y2 + z2 = 16 along a curve C.... Problem 55E: Cylinder and sphere Consider the sphere x2 + y2 + z2 = 4 and the cylinder (x 1)2 + y2 = 1, for z 0... Problem 56E: Flux on a tetrahedron Find the upward flux of the field F = x, y, z across the plane x/a+y/b+z/c=1... Problem 57E: Flux across a cone Consider the field F = x, y, z and the cone z2=(x2+y2)/a2 for 0 z 1. a.Show... Problem 58E: Surface area formula for cones Find the general formula for the surface area of a cone with height h... Problem 59E: Surface area formula for spherical cap A sphere of radius a is sliced parallel to the equatorial... Problem 60E: Radial fields and spheres Consider the radial field F=r/|r|p, where r = x, y, z and p is a real... Problem 61E: Heat flux The heat flow vector field for conducting objects is F = kT, where T(x, y, z) is the... Problem 62E: Heat flux The heat flow vector field for conducting objects is F = kT, where T(x, y, z) is the... Problem 63E Problem 64E: Flux across a cylinder Let S be the cylinder x2 + y2 = a2, for L z L. a.Find the outward flux of... Problem 65E: Flux across concentric spheres Consider the radial fields F=x,y,z(x2+y2+z2)p/2=r|r|p, where p is a... Problem 66E: Mass and center of mass Let S be a surface that represents a thin shell with density . The moments... Problem 67E: Mass and center of mass Let S be a surface that represents a thin shell with density . The moments... Problem 68E: Mass and center of mass Let S be a surface that represents a thin shell with density . The moments... Problem 69E: Mass and center of mass Let S be a surface that represents a thin shell with density . The moments... Problem 70E: Outward normal to a sphere Show that |tutv|=a2sinufor a sphere of radius a defined parametrically by... Problem 71E: Special case of surface integrals of scalar-valued functions Suppose that a surface S is defined as... Problem 72E: Surfaces of revolution Suppose y = f(x) is a continuous and positive function on [a, b]. Let S be... Problem 73E: Rain on roofs Let z = s(x, y) define a surface over a region R in the xy-plane, where z 0 on R.... Problem 74E: Surface area of a torus a.Show that a torus with radii R r (see figure) may be described... Problem 75E: Surfaces of revolution single variable Let f be the difference and positive on the interval [a, b].... format_list_bulleted
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,