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Math 152 (Spring 2009, Bates) Lab 4 Due March 10, 2009 1. Let f (x) = x4 − 3x3 + 9x + 5 and g(x) = x5 − x3 + 2x2 + 8. (a) (1 point) Make these two assignments in Maple (as functions, not expressions), and plot them without specifying a range for x. (b) (1 point) Now zoom in (by specifying a range for x) so that you can see three points of intersection. (c) (1 point) Use fsolve to find the x coordinate for these three points. (d) (2 points) Plot both curves and (using pointplot rather than geometry) all three points on the same axes, with the three points made larger and more colorful than the default so that they are clearly noticeable. 2. You are going to make a pretty necklace (sorry, men). (a) (1 point) Recall that an ellipse with axis lengths l1 , l2 can be given in parametric form as (l1 sin(t), l2 cos(t)). Pick some nice integers between 1 and 10 for the lengths and plot such an ellipse – make it gold with thickness 3 or more. (b) (2 point) Using this parameterization, it should be reasonable now to define three lists of 10 points each (using sequences) such that the points are nicely distributed on your ellipse/chain and alternate (list 1 point, list 2 point, list 3 point, list 1 point, etc.) as you go around the ellipse. (c) (1 point) Use the geometry package or the pointplot package to plot/draw your three sets of points (each with a different color and solid shape, and with a size large enough that you can see the points easily (at least 25)). (d) (1 point) Put it all together to make a necklace. (The spacing doesn’t have to be perfect, but please make sure that the axes are turned off....) (0 points from me) Export your last image as a jpeg and send it to somebody who would give you points for it.... 1