Maple #3 is due Tuesday 1 Feb 2000 For FULL credit STAPLE your sheets together. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ You are to plot the five functions below. Each plot must be rotated to a "nice" position and "look good (smooth)" . Each plot must have include axes and the title must include your name and what was plotted. Note that the expressions below are not necessarily in a form that Maple likes. Be sure to answer the questions in #1. 1. Again we are plotting f(x,y) = x y but this time it is with another function g(x,y)=x^2-y^2 and with the contourplot command (not contourplot3d). (For the domain use -L < x, y AND z < L for interesting value of L) What is the relationship between the contours lines of f and the contour lines of g. 2 & 3 The following function is from a Matlab demo. f(x,y)= 3(1-x)^2 e^(-x^2-(y+1)^2) - 10(x/5-x^3-y^5)e^(-x^2-y^2) -(1/3)e^(-(x+1)^2-y^2). [Remember, either define e:=exp(1) or replace e^x with exp(x). A common error is to replace e^x with exp^x, and unfortunately Maple doesn't notice the error, and does something dumb.] (For the domain use -L < x, y < L for an interesting L. Show all the features and not a lot of extra flatness.) Get two graphs for this function, a plot3d (#2) and an a "filled" contourplot (#3). 4. Use "arrow" to illustrate how the vector <3,2,3> is the vector sum of <3,0,0>,<0,2,0> and <0,0,3>. [hint: with(plottools) and display.] 5. Given three vectors u, v, and w and X= have Maple derive the equation of the plane through the "endpoints" of the vectors u, v, and w. Do the calculation once with the vectors u:=vector([3,0,0]);v:=vector([0,2,0]);w:=vector([0,0,1)); and once with u:=vector([u1,u2,u3]);v:=vector([v1,v2,v3]);w:=vector([w1,w2,w3));