AN92 Answers: Chapter 12 4. = = − = x y z 1 3 , 2, 0 or ( ) − 1 3 , 2, 0 5. − − − − − ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ 4 5 1 2 1 0 1 5 5 0 25 10 6. + + = − + + = − + + =− ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ + + = − + = − + + =− ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y z x y z x y z x y z x z x y z 3 2 4 6 1 0 8 2 2 1 3 11 or 3 2 4 6 8 2 2 3 11 7. − ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ 6 4 1 11 5 12 8. − − − − ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ 11 19 3 5 6 22 9. − − ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ 4 10 26 1 11 2 1 26 3 10. − ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 16 17 3 10 11. − − ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ 2 1 5 2 3 2 12. − − − − − ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ 3 3 4 2 2 3 4 5 7 13. = = x y 1 2 , 3 or ( ) 1 2 , 3 14. = − + x y 1 4 7, where y is any real number, or { } ( ) = − + x y x y y , 1 4 7, isanyrealnumber 15. = = − = x y z 1, 2, 0 or ( ) − 1, 2, 0 16. Inconsistent 17. −29 18. −12 19. = − = − x y 2, 5 or ( ) − − 2, 5 20. = = − = x y z 1, 1, 4 or ( ) − 1, 1, 4 21. ( ) − 1, 3 and ( ) 1, 3 22. ( ) 3, 4 and ( ) 1, 2 23. y 15 x 15 4x 2 3y 5 0 x2 1 y2 5 100 24. ( ) + + − + x x 3 3 2 3 2 25. ( ) ( ) − + + + + x x x x x 1 3 1 3 3 5 3 2 2 2 26. Unbounded y 9 x 9 2x 2 3y 5 2 x 1 2y 5 8 (4, 2) (8, 0) 27. The maximum value of z is 64, and it occurs at the point ( ) 0, 8 . 28. Jeans cost $24.50, camisoles cost $8.50, and T-shirts cost $6.00. Cumulative Review (page 852) 1. { } 0, 1 2 2. { }5 3. { } − − 1, 1 2 , 3 4. { } −2 5. { } 5 2 6. { } 1 ln 3 7. Odd; symmetric with respect to the origin 8. Center: ( ) − = 1, 2 ; radius 4 y 3 x 3 9. Domain: all real numbers Range: { } > y y 1 Horizontal asymptote: = y 1 y 5 x 5 y 5 1 (2, 2) 10. ( ) = − −f x x 5 2 1 Domain of f : { } ≠ − x x 2 Range of f : { } ≠ y y 0 Domain of { } ≠ −f x x : 0 1 Range of { } ≠ − −f y y : 2 1 11. (a) y 8 x 2 (22, 0) (0, 6) (b) y 1 x 1 (22, 0) (0, 2) (2, 0) (0, 22) (c) y 2 x 2 (0, 0) (1, 1) (21, 21) (d) y 2 x 2 (1, 1) (21, 21) x 5 0 y 5 0 (e) y 2 x 2 (1, 1) (0, 0) (f) y 2 x 2 (0, 1) y 5 0 (g) y 2 x 4 (1, 0) x 5 0 (h) y 1 x 1 , 0 2 !2 , 0 2 !2 2 5 !5 0, 2 5 !5 0, (i) y 1 x 2 (2, 1) (1, 0) (2, 21) (22, 21) (21, 0) (22, 1) 3 !3 y 5 x 3 !3 y 5 2 x (j) y 3 x 7 (3, 1) (1, 0) (21, 1) 1 4 2, 1 4 0, 12. (a) 10 210 210 10 ; −2.28 (b) Local maximum of 7 at = − x 1; local minimum of 3 at = x 1 (c) ( ] [ ) −∞ − ∞ , 1, 1, CHAPTER 12 Sequences; Induction; The Binomial Theorem 12.1 Assess Your Understanding (page 864) 5. sequence 6. T 7. T 8. b 9. summation 10. b 11. 3,628,800 13. 504 15. 1260 17. = = = = = s s s s s 1, 2, 3, 4, 5 1 2 3 4 5 19. = = = = = a a a a a 1 3 , 1 2 , 3 5 , 2 3 , 5 7 1 2 3 4 5 21. = = − = = − = c c c c c 1, 4, 9, 16, 25 1 2 3 4 5 23. = = = = = s s s s s 1 2 , 2 5 , 2 7 , 8 41 , 8 61 1 2 3 4 5 25. = − = = − = = − t t t t t 1 6 , 1 12 , 1 20 , 1 30 , 1 42 1 2 3 4 5 27. = = = = = b e b e b e b e b e 1 , 2 , 3 , 4 , 5 1 2 2 3 3 4 4 5 5 29. = + a n n 1 n 31. = − a 1 2 n n 1
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