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# CALCULUS 2 FOR ENGINEERS APPM 1360

GPA 3.76

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This 2 page Class Notes was uploaded by Dr. Filomena Hegmann on Thursday October 29, 2015. The Class Notes belongs to APPM 1360 at University of Colorado at Boulder taught by Anca Radulescu in Fall. Since its upload, it has received 37 views. For similar materials see /class/231866/appm-1360-university-of-colorado-at-boulder in Applied Math at University of Colorado at Boulder.

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Date Created: 10/29/15

APPM 1360 Due December 6 1995 Calculator Problems 7 Set 2 For each of the following problems use your calculator to plot the curves Graph the results on paper and clearly label your axis and tick marks lndicate appropriate values of t on the curves if they are parametric Be sure your calculator is in radians mode N 9 4 QTY The following curves should look like butter ies a 7 expcos 6 7 2cos 46 for 0 S 6 S 27r 9 b 7 expcos 6 7 2cos 46 sin5 for 0 S 6 S 247139 The parametric curve at cosat and y sinat is known as a Lissajous curve Plot this for a 3 and b 5 These functions played an important role in the science fiction movie industry during the 1950s and 19607s t t The parametric curve at a cost b cos and y asint bsin is known as a Hypotrochoid Plot this for a 8 and b 5 The curves defined by x a cost b cosct and y asint bsinct should remind you of Spirograph patterns Plot these curves for the following values a a5b10andc2 a a5b10andc4 b al2b6andc2 b al2b6andc4 Different parametric representations may give different segments of the same curve Graph the following curves in the any plane and discuss the similarities and differences a x72t2 andyl2t2 forallrealt 72tandyl2tfor allrealt T xtandylitforallrealt xlit2 andyt2 for allrealt x cos2t and y sin2t for all real 15 lnt7tandyltilnt fortgt0 OVER 6 Suppose two Ferris wheels are next to each other The motion of Sue on the first If Ferris wheel is described by the parametric equations 1 20 cos 7 and y1 t 20 20 sin for 0 S t Similarily Bob7s motion on the second Ferris wheel is t 15 described by 2 15 15 cos and y2 15 15sin o T 93 V CL V D V H gt Plot the paths of the two Ferris wheels Use the trace feature of your calculator to estimate how much time passes before both Bob and Sue are at one of the intersection points of the curves Use the trace feature of your calculator to estimate the first time that Bob and Sue are separated by the maximum distance possible Use the trace feature of your calculator to estimate the locations at which the curves intersect Report the any coordinates of these points as well as the values of t Use the calc feature of your calculator to estimate the slope dydx of each curve at the intersection point which is the highest above the ground Finally use the ntnt function on your calculator to estimate the arc length of the portion of the smaller Ferris wheel that overlaps the larger Ferris wheel

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