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spring2007 - MATH 1241 FINAL EXAM SPRING 2007 PART...

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Unformatted text preview: MATH 1241 FINAL EXAM SPRING 2007 PART I (Calculators Not Allowed) 1. If f ( x ) = (2 x 3 + 5) 7 , then f ′ ( x ) = (a) (6 x 2 ) 7 (b) 7 (6 x 2 ) 6 (c) 7 (2 x 3 + 5) 6 (d) 42 x 2 (2 x 3 + 5) 6 (e) 14 x 3 (2 x 3 + 5) 6 2. If f ( t ) = sin ( t 3 ), then f ′ ( t ) = (a) cos ( t 3 ) (b)- 3 t 2 cos ( t 3 ) (c) cos (3 t 2 ) (d)- cos (3 t 2 ) (e) 3 t 2 cos ( t 3 ) 3. If f ( x ) = 8 x 1 + x 2 , then f ′ ( x ) = (a) 8- 8 x 2 (1 + x 2 ) 2 (b) 8 (1 + 2 x ) 2 (c) 8 x 2- 8 (1 + x 2 ) 2 (d) 8 2 x (e) 8 + 24 x 2 (1 + x 2 ) 2 1 4. If f ( t ) = cos t- 3 e 2 , then f ′ ( t ) = (a)- sin t- 6 e (b) sin t- 6 e (c)- sin t (d) sin t (e)- sin t- 3 e 2 5. If f ( x ) = 6 √ x + 2 x , then f ′ ( x ) = (a) 6 √ x + 2 (b) 3 √ x- 2 x 2 (c) 6 √ x- 2 x 2 (d) 6 x + 2 (e) 3 √ x + 2 x 2 6. If f ( x ) = 2 x ( x 2- 4 √ x ), then f ′ ( x ) = (a) 6 x 2- 12 √ x (b) 2 parenleftbigg 2 x- 2 √ x parenrightbigg (c) 2 (2 x- 2 √ x ) (d) 6 x 2- 24 √ x (e) 6 x 2- 12 √ x 2 7. If f ( x ) = e x x 2 + 3 , then f ′ ( x ) = (a) e x 2 x (b) e x (2 x + 3) 2 (c) e x ( x 2- 2 x + 3) ( x 2 + 3) 2 (d) e x- 2 x ( x 2 + 3) 2 (e) e x ( x 2 + 2 x + 3) ( x 2 + 3) 2 8. If f ( x ) = 3 x 2 ln x , then f ′ ( x ) = (a) 6 x · 1 x (b) 6 x ln x + 3 x (c) 6 x ln x · 3 x (d) 6 x ln x (e) 3 x 9. If f ( x ) = 2 e 3 − x 2 , then f ′ ( x ) = (a) 2 e x (- 2 x ) (b) 2 e − 2 x (c) 2 e 3 − x 2- 2 x (d) 2 e x (3- x 2 ) (e) 2 e 3 − x 2 (- 2 x ) 10. lim x → 2 x 2 + x- 6 x- 2 = (a) ∞ (b) 5 (c) 2 (d) 0 (e) Does not exist . 3 11. lim x →∞ 3 x 2- 9 x- 5 x 2 = (a) 3 (b) ∞ (c)- 3 5 (d) 9 5 (e) 9 12. lim x → e 3 x- 1 x 3 = (a)- 1 3 (b) 0 (c) 3 2 (d) 9 2 (e) ∞ . 13. If f ( x ) = 2 x 3- 3 x 2 + 1, then the x-coordinate of the inflection point is: (a) x =- 2 (b) x = 2 (c) x =- 1 2 (d) x = 1 2 (e) x = 1 14. If f ( x ) = x 3- 3 x 2 + 6, then f ( x ) is decreasing on the interval(s): (a) (-∞ , 2) (b) (1 , ∞ ) (c) (0 , 1) (d) (0 , 2) (e) (-∞ , 0) ∪ (2 , ∞ ) 4 15. Let15....
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spring2007 - MATH 1241 FINAL EXAM SPRING 2007 PART...

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