Use Taylors formula to calculate linear and quadratic approximations to the function f(x,y) = sin(e^(x^2y^2)) at the point (0,0). Use your formulas to make two estimates of the value of f(0.01,0.01).

Compare the linear and quadratic estimates with the correct values. Repeat your estimate comparisons for f(0.1,0.1), f(0.5,0.5), and f(1,1). How good are your estimates? What goes wrong with the approximations as you move further from (0,0)? Sketch and label one or more contour plots to help explain your conclusions.