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Survey of Calculus Final Exam Review Key

# Survey of Calculus Final Exam Review Key - Survey of...

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Survey of Calculus Final Exam Review – Key Fall 2005 1. a. 6 b. –9 c. –1/4 2. a. 3 b. 3 c. 3 d. –1,2 e. –1, 0, 2 f. none g. –1, 0, 2 3. a. 4x-3 b. –1/x 2 4. y = -6x+2 5. a. 4 / 5 3 2 / 1 4 4 1 4 2 15 - - - - + - x x x x b. ) 8 )( 1 3 ( ) 2 ( 6 3 / 1 3 / 2 3 / 1 3 / 4 x x x x + + - c. ) 5 6 )( 5 2 ( ) )( 1 5 3 ( 2 / 1 2 / 1 2 - - + + - - x x x x x d. 2 / 3 2 / 1 2 / 1 2 1 2 9 - - - - x x x e. ( 29 2 2 1 2 2 ) 1 ( ) 2 )( ( 1 )( 1 + - - - - + - - x x x x x x f. 2 15 2 6 2 4 y x x y + - - g. x x x e x 3 3 2 2 2 1 2 - - + + h. 2 / 1 2 / 1 2 / 1 ) 1 ( 4 1 - - + x x i. [ ] [ ] 1 ) 2 ( ) 1 ( 3 ) 1 ( 4 2 2 3 3 2 - + - + x x x x 6. i. a. (3, -20), (-1, 12) b. Increasing: (-∞, -1), (3, ∞) Decreasing: (-1, 3) c. Rel Max: (-1, 12) Rel Min: (3, -20) d. (1, -4) e. Con Up: (1, ∞) Con Down: (-∞, 1) f. 6. ii. a. (0,0), (4, 256) b. Inc: (0,4) Dec: (-∞,0), (4,∞) c. Rel Max: (4, 256) Rel Min: (0,0) d. x = 0,3 e. Con Up: (0,3), (-∞,0) Con Down: (3,∞) f. 6. iii. a. (0, -1) b. Inc: (0,∞) Dec: (-∞,0) c. Rel Min: (0,-1) d. x = 0 e. Con Down: (-∞,0), (0, ∞) f. 7. a. C x x x x + + - - - 4 5 9 3 1 1 3 / 1 3 b. C x x + - 3 4 3 4 4 3 c. C x x + - 2 2 1 2 d. C t t + - - 2 / 3 2 / 7 4 6 e. C x e x + + ln 5 9 3 / 2 f. C x + + 2 / 3 2 ) 2 ( 3 1 g. C e x + 2 2 3 h. C x + - - 2 1 ln 2 1 i. C e x + 2 j. –1 k. 2 ln 2 1 l. C x x x + + - 2 / 1 2 / 3 2 / 5 4 4 2 x y -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -20 -10 0 10 20 x 1 0 2 0 x

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8. a.
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