Midterm1PracticeAnswers

Midterm1PracticeAnswers - t = 5 to time t = 9. 9. (a) The...

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Answers for Midterm 1 Practice 1. (a) 115 8 (b) 175 8 (c) 18 2. Note since 1 ln( x +1) 0 for all x 1, hence 1 ln( x +1) +1 1 for all x 1. Then by properties of the Riemann integral (discussed in the second lecture, see property 8 on pg 352 in the text) we have Z 196884 1 ± 1 ln( x + 1) + 1 ² dx 1(196884 - 1) = 196883 . 3. π 12 + 3 8 4. (a) 1 + x (b) - cos( x ) + x (c) 3 x 2 sin( x 3 2 ) - 2 x sin( x ), when x 0 (d) 2 x ln( x 2 +2 x 2 +1 ) 5. (a) arctan( x ) + C (b) ln | x - 3 | + C for x 6 = ± 3 (note that only x = 3 is bad for ln | x - 3 | , the only reason x = - 3 is excluded is that x +3 x 2 - 9 is not technically defined at x = - 3) (c) 5 x - 5 arctan( x ) + C (d) 2 3 x 3 2 + 2 e x 2 + C 6. (a) 4 11 (2 11 4 - 1) (b) 21 (c) 4 sin( π 16 ) (d) 3 π (e) 2 - 2 e - 1 7. (a) 4 3 (b) 14 3 - ln(4) (c) ln(2) - 3 8 (d) e + e - 1 - 1 8. (a) 1 2 ( e - 4 - 1) (b) 1 2 ( e - 4 + e - 1 ) (c) This is the change in velocity from time
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Unformatted text preview: t = 5 to time t = 9. 9. (a) The average of the function f on [ a,b ] is 1 b-a Z b a f ( x ) dx. (b) 1 4 (1-cos(4 2 )) (c) Yes. Since f is continuous on [0 , 2 ] the mean value theorem for denite integrals assures such a c exits. 10. (a) 1 6 (4 x-3) 3 2 + C , for x 3 4 (b) 1 4 ln | x 4 + 4 x | + C , for x 6 = 0 , 3 4 (c) e 1+ln( x ) + C , for x > (d) 1 3 (ln( x )) 3 + C , for x > (e) arctan( g ( x )) + C 11. (a) 8 5 (b) 1 8 ( e-1) (c) 1 2 (d) ln( 3) 1...
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This note was uploaded on 02/22/2010 for the course MATH Math 4B taught by Professor Alla during the Spring '10 term at UCLA.

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