General Instructions:

A. For the first page of each problem write the names of each of your group members in the upper right hand corner and write the problem number in the upper left hand corner.

B. You may work in groups of up to three students

C. Each problem will be submitted to a separate assignment on Gradescope. You should only submit one file per group per assignment.

D. When writing your answers please be sure to be legible.  You can use LATEX or another program to type you solutions.

E. When showing work for integrals you don’t need to write out u-substitution if the substitution formula is linear.

F. Each student started the semester with 2 tokens, and may exchange a token to re-do a homework problem.

1. To Pass this question you must:

(a) Compute the divergence of  . Be sure to pay attention to the domain of  .

(b) Compute the given line integral.

(c) Correctly determine whether  is conservative, and give a coherent explanation of how you arrived at your determination.

(d) Correctly determine whether a function  with the given properties exists, and give a coherent explanation of how you arrived at your determination.

(e) Show all relevant steps for each calculation.

(f) Present your work in a coherent manner.

2. To Pass this question you must:

(a) Correctly compute the surface integral in each case.

(b) Show all important steps in preforming these calculations.  These steps should be organized in a

coherent manner.

3. To Pass this question you must:

(a) Correctly compute the area of the region.

(b) Show all important steps in preforming these calculations.

(c) Present your work in a coherent manner.