Pre-Calc Homework Solutions 311

Pre-Calc Homework Solutions 311 - Section 7.4 /4 311 8. (a)...

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Unformatted text preview: Section 7.4 /4 311 8. (a) x sec2 y 1, so Length sec y dy. /3 10. y (b) (e x 2 e x) 3 , so Length 3 1 ex 2 e x 2 dx. (b) x so x sec2 y 1 tan y , 3 ln (cos y) ln (cos y) 0 y y 4 0 [ 3, 3] by [ 2, 12] (c) Length 11. y 3 0 20.036 2)1/2(2x) x x2 3 0 1 2 (x 2 2, so the length is x4 12. 2x 2 1 dx 1 3 0 (x x 2 1) dx 2)2 dx 1 3 x 3 [ 2.4, 2.4] by 2 , (x 2 3 2 3 x 0 2 (c) Length 9. (a) y 2.198 12. y 4 x, so the length is 3 2 2 4 sec x tan x, so /3 Length /3 1 sec x tan x dx. 2 2 1 0 x dx 0 1 8 1 27 80 10 27 (b) 9x dx 4 9x 3/2 4 8 4 0 . 13. x 3 y2 3 1 , 3 by [ 1, 3] (c) Length 3.139 14. x 2 1 , so the length is 4y 2 1 2 1 3 y2 dy y 3 4 y2 1 , so the length is 4y 3 3 1 1 y2 53 . 6 1 2 dy 4 y2 1 4y 3 1 y3 1 y3 1 1 2 dy 4 y3 2 1 y3 1 8y 2 1 2 dy 4 y3 2 1 1 4 y 4 123 . 32 15. x 2 y2 2 1 , so the length is 2y 2 y2 2 1 2 dy 2 y2 2 1 1 1 y2 2 1 2y 1 2 dy 2y 2 2 1 1 3 y 6 17 . 12 1 4(x 1)2 16. y x2 2x 1 4 (4x 4)2 (x 1)2 so the length is 2 1 0 2 (x (x 1)2 1)2 1 4(x 1 4(x 1 1)2 2 2 1)2 2 dx dx 53 . 6 0 1 (x 3 1)3 4(x 1) 0 ...
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