SalasSV_09_08_ex_ans

SalasSV_09_08_ex_ans - A-70 ANSWERS TO ODD-NUMBERED...

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Unformatted text preview: A-70 ANSWERS TO ODD-NUMBERED EXERCISES √ 23. (a) at (− 2 , ± 2 3); 3 9 (b) at (−1, 0) y (3,7) 21. (a) at (3, 7) and (3, 1); (b) at (−1, 4) and (7, 4) y 25. (a) at ( ± 1 2 √ 2, ±1); (b) at ( ± 1, 0) y 1 (–1,0) (–1,4) (3,1) (7,4) (–1,0) –2 3 x x –√2 2 √2 2 (1,0) x –1 27. y = 0, (π − 2)y + 32x − 64 = 0 29. The slope of OP is tan θ1 . The curve r = f (θ ) can be parametrized by setting x(θ ) = f (θ ) cos θ , Differentiation gives x (θ ) = −f (θ ) sin θ + f (θ ) cos θ , If f (θ1 ) = 0, then x (θ1 ) = −f (θ1 ) sin θ1 , Since f (θ1 ) = 0, we have m= y ( θ1 ) 1 = − cot θ1 = − . x ( θ1 ) slope ofOP y (θ1 ) = f (θ1 ) cos θ1 . y (θ ) = f (θ ) cos θ + f (θ ) sin θ . y(θ ) = f (θ ) sin θ . 31. y 33. y 35. y (0,1) x x x 37. −8 39. 2 41. 1 sin3 t 43. y − 2 = − 16 (x − 1 ) 3 8 SECTION 9.8 √ 1. 5 3. 7 √ 5. 2 3 7. 4 3 9. 6 + 1 ln 5 2 11. 63 8 13. ln (1 + √ 2) 15. √ 3 2 17. 1 π 3 + 1 2 √ 3 √ √ 19. initial speed 2, terminal speed 4; s = 2 3+ ln (2 + 3) √ √ √ 23. initial speed 2, terminal speed 2 eπ ; s = 2(eπ − 1) 21. initial speed 0, terminal speed 25. 8a 13; x = 1 (13 27 √ 13 − 8) 29. 2π 27. (a) 24a (b) use the identities cos 3θ = 4 cos3 θ − 3 cos θ , sin 3θ = 3 sin θ − 4 sin3 θ √ √ √ 4π 1 1 7 33. 2 5(e − 1) 35. 4 − 2 2 37. ln (1 + 2) 39. c = 1 41. (a) ( 2 , − 2 ) 43. L = a b√ 31. √ 2(e4π − 1) 1 + sinh2 x dx = a b√ cosh2 x dx = a b cosh x dx = A 45. L ∼ 4. 6984 = 47. (a) y (b) 2.7156 x 49. 4 51. (b) 28.3617 53. 1 + [ f (x)]2 = 1 + tan2 [α (x)] = | sec [α (x)]| ...
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