EXERCISES

1. Compute the four second order partial derivatives of the following functions using the indicated Maple command.
   1. f(x,y) = exp(x² + y²)   using diff.
   2. g(x,y) = 4 tan(x²y) (x²+y²)/(x+y)^1/2   using D.
   
   Notice the effect of symmetry in (a). Also imagine what fun it would be to compute (b) by hand.

2. Consider the function f(x,y) = sqrt(|xy|) and the surface z = sqrt(|xy|) Where is this function continuous; where is it discontinuous? Where is this function not differentiable? Where does the surface not have a unique tangent plane? In terms of our discussions in class, please explain your answers to these questions. Also plot the tangent plane at (x,y,z) = (1,1,1). [This question is similar to Widder, #19, p. 19.]