Differentials and first-order approximation For problems #1-#4 below, compute the differential and first-order approximations of the function at the given point. 1. The function f(x, y) = et cos(y) at (ro, yo) = (0, 0). 2. The function f(x, y) = x In(x2 + y2 + 1) at (20, yo) = (1, 0). 3. The function g(x, y) = sin(xy + 1) + x2y at (20, yo) = (-1, 1). 4. The function k(x, y) = (x, y) # (0, 0) (x, y) = (0,0) at the point (To, yo) = (0, 0). 5 (no submission). For #1-4 above, plot both the function and the first-order approximation on Cal- cPlot3D. For #1-3, convince yourself that the plane this shows is a good approximation to the graph of the function; for #4, convince yourself that it is not a good approximation. Do not submit anything; I just want you to see these examples yourself. Remark 1. There are two settings that may be useful. One, pressing the magnifying glass makes the surfaces 'transparent', and usually easier to see. Two, if you press the black eight-pointed wheel below a given function, it lets you change the x- and y- intervals it plots. You may wish to restrict the graph of the first-order approximation to a small neighborhood of (To, yo). For instance, in #3, you might use the interval from -1.5