# E4RevAns - ,e 5 decreasing on e 5 ∞ always concave down...

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Review Answers – Exam 4 1. Answers from left to right Row 1: 2 ln | 1 + x | + 2(1 + x ) - 1 + C 1 2 ln | e 2 x - 4 | - 2( e 2 x - 4) - 1 + C 3 2 sec(2 x ) - 3 2 ln | sec 2 x | + C Row 2: 64 3 2 3 x 3 2 + 2 x + 2 x + C 98 3 Row 3: 1 2 ( e 3 - e - 1 ) 3 2 ( 3 4 - 1) 2 tan( x ) + 2 sec( x ) - x + C ( Recall tan 2 ( x ) = sec 2 ( x ) - 1 ) Row 4: 1 6 ( e x + e ) 6 + C - 32(4 - x ) 1 2 + 16 3 (4 - x ) 3 2 - 2 5 (4 - x ) 5 2 + C 1 ln(5) 5 x + 3 tan - 1 ( x ) - 1 2 e x 2 + C 2. a) False b) False 3. 11 6 - 4 3 h cos( t 2 ) i 3 4. 72 ln(3) - 100 3 5. 45 6. x sin( x 2 ) - 2 x 2 sin( x 4 ); e ; does not exist 7. 3 π 4 8. 5 + 40 π + 10 ln | ln(4) - 2 2 | (approximately 6) 9. a) 237 850 b) 152 425 c) 1 2 ln(2) 10. lim n →∞ n X i =1 h 1 + (1 + 2 i n ) 3 i 2 n = 22 11. G 0 ( e ) = 8; increasing on ( 0

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Unformatted text preview: ,e 5 ); decreasing on ( e 5 , ∞ ); always concave down 12. m =-1; M = 2;-4 ≤ R 2-2 f ( x ) d x ≤ 8 13. 25 3-2 ln(2) 1 14. Displacement:-60 + 9 ln(21) ; Total distance: 108 + 9 ln( 27 7 ) 15. c = e-1 16. Area= 2; Deﬁnite integral= 2 3 17. Min at x = 6; Max at x = 3; Max value is 7; Min value is 1 2...
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E4RevAns - ,e 5 decreasing on e 5 ∞ always concave down...

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