Pre-Calc Homework Solutions 426

Pre-Calc Homework Solutions 426 - 426 70(a Section 10.6...

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Unformatted text preview: 426 70. (a) Section 10.6 Section 10.6 Exercises 1. [ 9, 9] by [ 6, 6] dy dx f ( ) sin f ( ) cos cos cos 2 sin cos2 sin cos cos sin2 1 1 f ( ) cos f ( ) sin ( 1 ( 1 cos sin sin )cos sin )sin The graphs are parabolas. (b) As k 0 , the limit of the graph is the negative x-axis. s Section 10.6 Calculus of Polar Curves (pp. 559568) Quick Review 10.6 dy dy/dt 5 cos t dx dx/dt 3 sin t 5 2. cot 2 0.763 3 dy dx dy dx dy dx 1, 0 dy dx 1 1 1 cos 2 cos . cos 2 sin 0 1 2. 5 cot t 3 f ( ) sin f ( ) cos f ( ) cos f ( ) sin 2 sin 2 sin 2 sin 2 cos 1. 0 1 dy , which is undefined; 0 dx 1 , which is undefined. 0 f ( ) cos f ( ) sin sin cos (2 (2 3 sin ) cos 3 sin ) sin cos sin2 ) 2 , 3 0 1 0; /2 3. Solve cot t 0: t 2 or 3 ; 2 2 and , 5 sin 2 dy dx f ( ) sin f ( ) cos 3 cos 3 cos 2 cos 2 sin the corresponding points are 3 cos 3 3 and 3 cos , 5 sin 2 2 (0, 5) 3. dy dx (0, 5) 0, , or 2 ; 4. 5 cot t is undefined when t 3 the corrresponding points are (3 cos 0, 5 sin 0) (3 cos , 5 sin ) (3 cos 2 , 5 sin 2 ) ( 3, 0). dy 2 dt dt 6 sin 3(cos2 2 3 (3, 0) and dy dx (2, 0) dy dx ( 1, /2) dy dx (2, ) dy dx (5, 3 /2) dy dx dy dx dy dx dy dx 0 5. Length 0 dx 2 dt dy dx 0, /2 9 sin2 t 0 25 cos2 t dt, 12.763. 2 , and 3 0 5 which using NINT evaluates to For questions 68, the graph is: 0. 3 /2 4. f ( ) sin f ( ) cos 3 sin2 3 sin cos f ( ) cos f ( ) sin 3 cos (1 cos ) 3 sin (1 cos ) [ 2, 4] by [ 2, 2] 3 cos 6 sin 1 2 3(cos2 sin2 ) cos 3 sin 1 2 3 2 1 2 3 2 3 2 6. The upper half of the outer loop 7. The inner loop 8. The lower half of the outer loop 9. y 0 for x 6 dy dx (1.5, /3) , which is undefined; 1 2 3 2 0 or 6. x 2) dx 3x 2 1 3 6 x 3 0 Area 0 (6x 36 dy dx (4.5, 2 /3) 0; 10. Use a graphing calculator's intersect function to find that the curves cross at x NINT to find 2.248 0.270 and x 2.248, then use dy dx (6, ) dy dx (3, 3 /2) 1 1 , which is undefined; and 0 0 0 0 ( 1) ( 1) Area 0.270 [2 sin x (x 2 1. 2x 1)] dx 2.403. ...
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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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