finalreviewanswerf11

finalreviewanswerf11 - SOLUTIONS 1(a tan C 3 2(b 2 3(c 6...

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SOLUTIONS 1. (a) tan θ + C (b) 3 2 - 2 π 3 (c) π 6 2. (a) 3 2 ln | x 2 - 4 | + C (b) 3 x 2 + 2 x + 5 + C (c) 3 + 3 2 (d) 62 3 (e) ln | 1 + sin 2 x | + C (f) arctan(sin x ) + C (g) 1 (h) ln | sin x | + C (i) - 1 2 e 1 2 x - 1 + C (j) - 32 15 (k) e x - 1 + ln | e x - 1 | + C or e x + ln | e x - 1 | + C (l) 1 - cos(1) 0 . 4597 3. minimum value on [ - 2 , 2] = - 1; maximum value on [ - 2 , 2] = 2 - 4 Z 2 - 2 3 p x 2 + 2 xdx 8 by the Comparison Properties of the integral. 4. (a) i. Z ( x + 1) 2 x dx = Z x + 2 x + 1 x dx = Z ± x + 2 + 1 x ² dx = 2 3 x 3 + 2 x + 2 x + C ii. Z ( x + 1) 2 x dx = Z 2 u 2 du, where u = x + 1; 2 du = 1 x dx = 2 u 3 3 + C 2( x + 1) 3 3 + C = 2 3 ³ x 3 2 + 3( x ) 2 + 3 x + 1 ´ + C = 2 3 x 3 + 2 x + 2 x + 2 3 + C = 2 3 x 3 + 2 x + 2 x + C 0
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(b) f ( x ) = 2 3 x 3 + 2 x + 2 x - 2 3 5. (a) x ln x ; (b) xe 2 x ; (c) e 6. - x sin x 2 7. f ( x ) = - 4 3 cos 3 ± x 2 ² + 7 3 8. 35 3 9. (a) 2 3 ln ± 5 2 ² ; (b) 1 5 10. (a) 36; (b) 20 units 2 11. Z 3 0 x p 1 + x 2 dx ; 1 3 (10 3 2 - 1) 12. (a) L 4 = 139 306 0 . 4542; (b) M 4 = 385376 694089 0 . 5552; (c) Area = 1 2 ln 3 0 . 5493 13. R ( x ) = 200 x + 0 . 2 x 2 + x 3 - 8 , 800; P ( x ) = x 3 + 0 . 1 x 2 + 180 x - 10
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This note was uploaded on 02/14/2012 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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finalreviewanswerf11 - SOLUTIONS 1(a tan C 3 2(b 2 3(c 6...

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