Math 209Midterm — Solutions1. Either compute the following limit or show that it does not exist:lim(x,y)→(0,0)px2y2+ 1-1x2+y2.
2.(a) Letu(x, y, z) =eax+4ycos(5z). Find all values of the constant “a” which make the following true:
(b) Find∂z∂xand∂z∂yat the pointP: (1,ln 2,ln 3) ifxey+yez+ 2 lnx-2-3 ln 2 = 0.Solution
