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# review4answerf11 - Â 1 4 â€¦ 1 3258 16(a 1 2 â€¦ 3(b 15 17...

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MAC 2311 Test Four Review, Fall 2011 - Answers 1. (a) e (b) 1 p e 2. Horizontal asymptote: y = 0 ( lim x !¡1 f ( x ) = 1 but lim x !1 f ( x ) = 0 using L’Hospital’s Rule). Local maximum: (2 ; 4 e 2 ), no local minimum; in ection points at x = 2 § p 2 3. lim x ! 0 + f ( x ) = 0 using L’Hospital’s Rule and lim x !1 f ( x ) = 1 , so graph has a hole at (0 ; 0) and no asymptotes. No local maximum, local minimum is f ( e ¡ 1 = 2 = ¡ 1 2 e , and the in ection point is ( e ¡ 3 = 2 ; ¡ 3 2 e 3 ). 4. (a) 2 3 p x 3 + 2 x + 2 p x + C (b) ¡ cos x + sec x + C (c) x 3 3 ¡ 2 arctan x + C 5. a) false; Z f ( x ) dx = 1 6 f ( x ) + C b) false; Z x 1 g 0 ( t ) dt = g ( x ) ¡ g (1) (Fundamental Theorem part II) d dx Z x 1 g ( t ) dt = g ( x ) (Fundamental Theorem part I) c) false 6. f ( x ) = x 2 2 ¡ 6 p x + 11 2 7. 5 2 + 2 8. ¡ 2 + 2 e 9. absolute maximum (1 ; 1 e ); absolute minimum (0, 0); 0 Z 3 0 xe ¡ x dx 3 e 10. g 0 ( e ) = 1 + 2 e ; g is increasing on (0 ; 1 ); g is never decreasing

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11. ¡ p x 2( x + 2) 12. (a) 35; (b) ¡ 24; (c) 28 sq. units 13. Z 3 0 p 1 + x 2 dx 14. Z 3 1 ( x 2 ¡ 2 x ) dx = lim n !1 n X 1=1 2 n (1 + 2 i n ) 2 ¡ 2(1 + 2 i n ) = 2 3 15. (a) Area 1 + 1 2 + 1 5 + 1 10 = 1 : 8 (b) Area 4 5 + 4 13 + 4 29 + 4 53 1 : 32 (c) Area = tan
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Unformatted text preview: Â¡ 1 4 â€¦ 1 : 3258 16. (a) 1 2 + â€¦ 3 ; (b) 15 17. v ( t ) = 1 2 e 2 t + 5 2 in meters/sec; s ( t ) = 1 4 e 2 t + 5 2 t + 7 4 in meters 18. 80 ft/s 19. 2 3 ft by 20 3 ft by 5 3 ft 20. Dimensions: x = 550 ft, y = 2200 3 ft 21. ( Â¡ 4 ; 2), (4 ; 2) 22. Assume the base of the triangle is a leg, not the hypotenuse with point ( x;y ) in the ï¬‚rst quadrant; x = 1, y = p 3, A = 3 p 3 2 23. Dimensions: x =5 ft and y =10 ft 24. relative maximum: f ( Â¡ 2) = 0, relative minimum: f (0) = Â¡ 2 2 3 , vertical tangent line and inÂ±ection point at (1 ; 0) 25. relative minimum: f ( Â¡ p 3) = 3 p 3 2 and relative maximum: f ( p 3) = Â¡ 3 p 3 2 ; inÂ±ection point (0 ; 0)...
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