Pre-Calc Homework Solutions 401

Pre-Calc Homework Solutions 401 - Section 10.1 Quick Review...

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Unformatted text preview: Section 10.1 Quick Review 10.1 1. (cos (0), sin (0)) 2. cos 3. x 2 3 3 , sin 2 2 dy dx d 2y dx 2 dy dx dy/dt dx/dt dy /dt dx/dt 0 sin t 3 sin t sin t 401 2. (a) (b) 1) 3. (a) y 3 (1, 0) (0, 1) sin2 t 0 y2 1 (since cos2 t 4. The portion in the first three quadrants, moving counterclockwise as t increases. 5. x t, y t2 1, 1 t 3 6. The graph is a circle with radius 2 centered at (2, 3). Modify the x cos t, y sin t parameterization correspondingly: x 2 cos t 2, y 2 sin t 3, 0 t 2 . 7. dy dx dy/dt dx/dt 3 cos t , 2 sin t 3 3( equals 4 2( 3 ,x 4 2/2) 2/2) 3 . 2 y dy/dt dx/dt 3/(2 3t) 1/(2 t 1) 3 t 1 3t 3 d 2y dx 2 dy /dt dx/dt 3 t 3/2 3 t 3/(2t 2 3 1/(2 t 3/t) 1) 3 t t2 3 1 3/t (b) which at t 3 8. y x C. For t 2 3 2 3 ( 2) 2 2 3 Thus, y x 3 2 2 and y 3 2. 3 2 2 , so 4. (a) (b) C and C 2. 3 ,x 4 dy dx d 2y dx 2 dy dx d 2y dx 2 y dy/dt dx/dt dy /dt dx/dt 1/t 1/t 2 1 1/t 2 t t2 9. y 3 2 2 2 x 3 C. For t 2 ( 3 2 x 3 2 and y 5 6 2 3 2 , so 2 5. (a) (b) y dy/dt dx/dt 3t 2 2t 3 2) C and C . Thus, y 3 2 5 2 . 6 dy /dt dx/dt [(2t 3)(6t) 12t 2 18t (2t 3)3 6t 2 18t (2t 3)3 (3t 2)(2)]/(2t 2t 3 6t 2 3)2 10. y x, so 3 Length 0 3 1 1 0 3 2 2 x dx 6. (a) 3 0 9 x dx 4 9 3/2 x 4 313/2 8 . 27 dy dx d 2y dx 2 y dy/dt dx/dt 2t 2t 1 1 8 1 27 (b) dy /dt dx/dt [(2t 1)(2) 4 (2t 1)3 cos t sin t Section 10.1 Exercises 1. (a) (b) dy dx d 2y dx 2 (2t 1)(2)]/(2t 2t 1 1)2 y dy/dt dx/dt dy /dt dx/dt 2 sin t 4 cos t 1 sec2 t 2 1 tan t 2 1 sec3 t 8 7. 4 cos t dy dx dy/dt dx/dt cot t k (k any integer). Then k , 1 sin 2 (a) cot (x, y) (2, 0 when t 2 1 cos 2 2 k 2). 1). The points are (2, 0) and (2, (b) cot is undefined when t (x, y) (2 cos (k ), 1 k (k any integer). Then sin (k )) 1). (2 1, 1). The points are (1, 1) and (3, ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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