FDWKCalcSM_ch8

FDWKCalcSM_ch8 - 350 Section 8.1 51. y = sec 2 x , so the...

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350 Section 8.1 51. ′ = yx sec 2 , so the area is 21 2 2 0 4 π tan sec , xx d x () + which using NINT evaluates to 384 .. 52. x = 11 2 1 1 1 22 y x y y y and so thearea is ′=− +− , 2 1 2 dy , which using NINT evaluates to 5.02. 53. (a) The two curves intersect at x = 1.2237831. Store this value as A. Area = (s i n s e c ) 2 1 366 0 = d x A (b) Volume = i n )( s e c ) 2 16 404 0 = d x A (c) Volume = i e c ) 2 1 629 2 0 = d x A 54. (a) Average temp = ≈° 1 14 6 80 10 12 87 6 14 cos . t dt F (b) Ft t cos =− 80 10 12 78 for 5 2308694 18 766913 . ≤≤ t Store these two values as A and B . (c) Cost 005 80 10 12 78 5 10 . cos . t dt A B The cost was about $5.10. 55. (a) 15600 24 160 6004 2 9 17 tt dt −+ people. (b) 15 15600 24 160 16 2 9 17 2 ( dt + 0 104 048 17 23 ) , dollars (c) =−≈ HE L () () () 17 17 17 380 people. H (17) is the number of people in the park at 5:00, and H 17 is the rate at which the number of people in the park is changing at 5:00. (d) When =−= Ht E t L t ; 0 that is, at t = 15.795 Chapter 8 Sequences, L’Hôpital’s Rule, and Improper Integrals Section 8.1 Sequences (pp. 435–443) Quick Review 8.1 1. f 5 5 53 5 8 == + 2. f −= 2 2 23 2 3. −+ − = 231 1 51 ( . ) 4. = 751 35 ( ) 5. 15 2 12 41 .( ) = 6. 215 45 31 (. ) . 7. lim lim x x →∞ + + 52 6 5 3 0 32 42 3 4 8. lim sin( ) lim x x x x →→ 00 33 3 9. lim sin lim x x x x = = 1 10. lim . x x x x + + 2 1 2 3 Does not exist, or Section 8.1 Exercises 1. 1 2 2 3 3 4 4 5 5 6 6 7 50 51 ,,,,,; 2. 2 5 2 8 3 11 4 14 5 17 6 149 50 ,,, , , ; 3. 2 9 4 64 27 625 256 7776 3125 2 48832 ,, , , . , 117649 46656 2 521626 51 50 2 691588 50 ., . 4. −− 2 2 0 4 10 18 2350 , ,,, , , 5. 31 1 3 11 ,, , ; −−− 6. 0 1 5 ,, , ; 7. 2 4 8 16 256 ,,, ; 8. 10 11 12 1 13 31 19 487171 10 1 1 7 , , ., . ; . (.) 9. 112321 ,, ,; 10. 32 112 11. (a) 3 (b) ad += + = 72 7 3 1 9 (c) aa nn =+ 1 3 (d) an n n =− + = 3 3 5 ( ) 12. (a) 2 (b) +=+−= 71 5 7 (c) 1 2 (d) n n =+−−= 15 1 2 2 17 ( ) 13. (a) 1 2 (b) + = 7 1 2 9 2
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Section 8.1 351 13. Continued (c) aa nn =+ 1 1 2 (d) an n n =+ − = 11 1 2 1 2 () + 14. (a) 0.1 (b) ad += + = 73 7 0 13 7 (.) . (c) 1 01 . (d) n n = + 3 1 01 29 ( . ). . 15. (a) 1 2 (b) 8 1 2 0 03125 8 = . (c) = 1 2 1 (d) a n n n = = 8 1 2 2 1 4 16. (a) 15 . (b) ()(.) . 1 1 5 25 6289 8 (c) = 1 (d) a n == −− 115 17. (a) 3 (b) , −= 3 19 683 9 (c) =− 3 1 (d) a n =− − 33 3 1 18. (a) 1 (b) ( ) 51 5 8 (c) 1 (d) a n n 51 1 19. 72 3 3 = a 1 23 5 =− − =− n 1 32 for all 20. = 35 4 2 a 1 52 41 3 =−− = ( ) n n =+−−= −+ 13 1 2 2 15 ( ) 21. r = = 3010000 3010 10 / a 1 3 3010 10 301 . n n =≥ 30110 1 1 .() , 22. r = = 16 12 2 / / a 1 2 14 = = / / n () ( ) , 1 23. [0, 20] by [0, 1] 24. [0, 20] by [–1, 1] 25. [0, 20] by [–5, 5] 26. [0, 20] by [0, 10] 27. [0, 10] by [–25, 200] 28. [0, 10] by [–5, 30]
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352 Section 8.1 29. [0, 20] by [–1, 5] 30. [0, 10] by [–15, 10] 31. lim lim ( ) lim nn n n →∞ →∞ →∞ + =+ == 31 3 1 30 3 converges, 3 32.
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This note was uploaded on 09/26/2010 for the course MATH 135 taught by Professor Noone during the Summer '08 term at Rutgers.

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FDWKCalcSM_ch8 - 350 Section 8.1 51. y = sec 2 x , so the...

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