Optics 287, Math 287March 19, 200911:05 to 12:20Midterm Exam1.a) Calculate the gradient, divergence or curl (whichever applies) ofA(r)=rnr,where nis an integer. (15 pts.)b) For what values of nis the divergence constant? (5 pts.)c) For what values of nis the divergence equal to zero? (5 pts.)d) For what values of nis the curl zero? (5 pts.)e) Consider the integral of the divergence of Aover the volume contained in aunit sphere centered at the origin. What is the value of this integral for any n?(10 pts.)2.(15 pts) Consider the functionf(x)=1−x,0≤x<1,−1−x,−
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