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Rog_Sec_13_1-11_1

Rog_Sec_13_1-11_1 - Math 20C Lecture Examples Sections 11.1...

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(7/25/08) Math 20C. Lecture Examples. Sections 11.1 and 13.1. Parametric equations and vector-valued functions Example 1 Draw the curve C : x = x ( t ) , y = y ( t ) , 0 t 3 in an xy -plane, where x = x ( t ) and y = y ( t ) are the piecewise-linear functions with graphs in Figures 1 and 2. t 1 2 3 x 10 20 30 x = x ( t ) t 1 2 3 y 10 20 30 y = y ( t ) FIGURE 1 FIGURE 2 Answer: Use the values in the table below. Figure A1 t 0 1 2 3 x = x ( t ) 10 10 30 10 y = y ( t ) 10 30 10 10 x 10 20 30 y 10 20 30 braceleftbigg x = x ( t ) y = y ( t ) t = 0 , 3 t = 2 t = 1 Figure A1 Lecture notes to accompany Sections 11.1 and 13.1 of Calculus, Early Transcendentals by Rogawski. 1
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Math 20C. Lecture Examples. (7/25/08) Sections 11.1 and 13.1, p. 2 Example 2 Sketch the curve C : x = t 3 - 12 t, y = 2 t 2 , - 4 t 4. Answer: Draw x = x ( t ) in a tx -plane and y = y ( t ) in a ty -plane for - 4 t 4 (Figures A2a and A2b). Use these graphs to draw C : x = t 3 - 12 t, y = 2 t 2 , - 4 t 4 in an xy -plane. Figure A2c t - 4 - 2 0 2 4 x = t 3 - 12 t - 16 16 0 - 16 16 y = 2 t 2 32 8 0 8 32 t 4 - 2 x 20 - 20 - 4 2 t 2 4 - 2 - 4 y 10 20 30 x ( t ) = t 3 - 12 t y ( t ) = 2 t 2 - 4 t t - 4 t 4
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