Problem 1E: Vector Field Define a vector field in the plane and in space. Give some physical examples of vector... Problem 2E Problem 3E: Potential Function Describe how to find a potential function for a vector field that is... Problem 4E Problem 5E Problem 6E: In Exercise 5-8, match the vector field with its graph. [The graphs are labeled (a), (b), (c), and... Problem 7E: In Exercise 5-8, match the vector field with its graph. [The graphs are labeled (a), (b), (c), and... Problem 8E: In Exercise 5-8, match the vector field with its graph. [The graphs are labeled (a), (b), (c), and... Problem 9E Problem 10E Problem 11E Problem 12E Problem 13E: Sketching a Vector Field In Exercises 9-14, find F and sketch several representative vectors in the... Problem 14E Problem 15E Problem 16E Problem 17E Problem 18E Problem 19E: Finding a Conservative Vector Field In Exercises 19-28, find the conservative vector field for the... Problem 20E Problem 21E Problem 22E Problem 23E: In Exercises 19-28, find the conservative vector field for the potential function by finding its... Problem 24E Problem 25E Problem 26E: In Exercises 19-28, find the conservative vector field for the potential function by finding its... Problem 27E: In Exercises 19-28, find the conservative vector field for the potential function by finding its... Problem 28E Problem 29E Problem 30E Problem 31E Problem 32E Problem 33E Problem 34E Problem 35E Problem 36E: In Exercises 29-36, determine whether the vector field is conservative. F(x,y)=yi+xj1+xy. Problem 37E: In Exercises 37-44, determine whether the vector field is conservative. If it is, find a potential... Problem 38E: In Exercises 37-44, determine whether the vector field is conservative. If it is, find a potential... Problem 39E Problem 40E Problem 41E Problem 42E Problem 43E Problem 44E Problem 45E: Find curl F for the vector field at the given point F(x,y)=(xyz)i+(xyz)j+(xyz)k;(2, 1, 3). Problem 46E: Find Curl F for the vector field at the point F(x,y)=(x2z)i(2xz)j+(yz)k;(2,-1,3). Problem 47E: Find Curl of the vector field F at the given point F(x,y)=(exsiny)i(excosy)j; (0, 0, 1). Problem 48E: Find Curl of the vector field F at the given point F(x,y)=exyz(i+j+k);(3, 2, 0). Problem 49E Problem 50E Problem 51E: Determine whether the vector field F is conservative. If it is, find a potential function for the... Problem 52E: Determine whether the vector field F is conservative. If it is, find a potential function for the... Problem 53E: Determine whether the vector field F is conservative. If it is, find a potential function for the... Problem 54E: Determine whether the vector field F is conservative. If it is, find a potential function for the... Problem 55E: Determine whether the vector field F is conservative. If it is, find a potential function for the... Problem 56E: Determine whether the vector field F is conservative. If it is, find a potential function for the... Problem 57E Problem 58E Problem 59E Problem 60E Problem 61E: Find the divergence of the vector field at the given point. F(x,y,z)=(xyz)i+(xz2)j+(3yz2)k; (2, 4,... Problem 62E: Find the divergence of the vector field at the given point. F(x,y,z)=(x2z)i(2xz)j+(yz)k; (2,-1,3). Problem 63E Problem 64E Problem 65E Problem 66E Problem 67E Problem 68E Problem 69E Problem 70E: In Exercise 69 and 70, find curl (FxG)=x(FxG) F(x,y,z)=xizk G(x,y,z)=x2i+yj+z2k Problem 71E Problem 72E: In Exercises 71 and 72, curl (curlF)=x(xF) F(x,y,z)=x2zi2xzj+yzk Problem 73E Problem 74E: Divergence of a Cross Product In Exercises 73 and 74, find div(FG)=(FG).... Problem 75E Problem 76E Problem 77E: In parts (a) - (h), prove the property for vector fields F and G and scalar function f. (Assume that... Problem 78E format_list_bulleted