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Pre-Calc Homework Solutions 426

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

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70. (a) [ 2 9, 9] by [ 2 6, 6] The graphs are parabolas. (b) As k 0 1 , the limit of the graph is the negative x -axis. Section 10.6 Calculus of Polar Curves (pp. 559–568) Quick Review 10.6 1. } d d y x } 5 } d d y x / / d d t t } 5 } 2 5 3 co si s n t t } 5 2 } 5 3 } cot t 2. 2 } 5 3 } cot 2 < 0.763 3. Solve cot t 5 0: t 5 } p 2 } or } 3 2 p } ; the corresponding points are 1 3 cos } p 2 } , 5 sin } p 2 } 2 5 (0, 5) and 1 3 cos } 3 2 p } , 5 sin } 3 2 p } 2 5 (0, 2 5) 4. 2 } 5 3 } cot t is undefined when t 5 0, p , or 2 p ; the corrresponding points are (3 cos 0, 5 sin 0) 5 (3 cos 2 p , 5 sin 2 p ) 5 (3, 0) and (3 cos p , 5 sin p ) 5 ( 2 3, 0). 5. Length 5 E p 0 ! 1 } § d d x § t } 2 § 2 § 1 § 1 § } d d § y t } 2 § 2 § dt 5 E p 0 ˇ 9 w s w in w 2 w t w 1 w 2 w 5 w c w o w s 2 w t w dt, which using NINT evaluates to < 12.763. For questions 6–8, the graph is: [ 2 2, 4] by [ 2 2, 2] 6. The upper half of the outer loop 7. The inner loop 8. The lower half of the outer loop 9. y 5 0 for x 5 0 or 6. Area 5 E 6 0 (6 x 2 x 2 ) dx 5 3 3 x 2 2 } 1 3 } x 3 4 5 36 10. Use a graphing calculator’s intersect function to find that the curves cross at x < 0.270 and
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