(Solved):     How do I deal with letter e? 2. (Section 7.9 and Unit 8) Consider the 3-dimension ...

 

 

How do I deal with letter e?

2. (Section 7.9 and Unit 8) Consider the 3-dimensional vector field F defined by F(x, y, z) = (2xyz, z²z+2y2², a²y + 2y²z+€²). (a) Write down the Jacobian matrix Jp (x, y, z). (b) Determine divE (a.y.z). (e) Determine curl E (a. y, z). (2) (d) Does E have a potential function? Give reasons for your answer, referring to the relevant definitions and theorems in the study guide. (2) (e) Find a potential function of F. using the method of Example 7.9.1. Note, however, that the example concerns a 2-dimensional vector field, so you will have to adapt the method to be suitable for a 3-dimensional vector field. Pay special attention to the notation that you use for derivatives of functions of more than one variable. (6)