review4answers11 - t 5 2 t 7 4 in meters 19 80 ft/s 20...

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MAC 2311 Test Four Review, Spring 2011 - Answers 1. increasing on (0, 4); decreasing on (4 ; 1 ) since the domain of f is (0 ; 1 ); local maximum at (4 ; 3 16 ); no local mimimum 2. increasing and concave down on ( ¡ 3 ; ¡ 1) in±ection points: ( ¡ 3 ; 10 e 3 ) and ( ¡ 1 ; 2 e ) 3. local minima at x = ¡ 2 and x = 5, local maximum at x = 1 in±ection points at x = 0 and x = 2 4. (a) ¡ 1 4 ; (b) 1 2 ; (c) 1 2 ; (d) e 2 ; (e) e ; (f) 0 5. 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 6. (a) 2 3 p x 3 + 2 x + 2 p x + C (b) ln j x j ¡ 5tan ¡ 1 x + C (c) ¡ cos x + sec x + C (d) tan ± + C 7. a) false; Z f ( x ) dx = 1 6 f ( x ) + C b) false; Z x 1 g 0 ( t ) dt = g ( x ) ¡ g (1) but d dx Z x 1 g ( t ) dt = g ( x ) c) false 8. f ( x ) = x 2 2 ¡ 6 p x + 11 2 9. 5 2 + 2 10. ¡ 2 + 2 e 11. absolute maximum (1 ; 1 e ); absolute minimum (0, 0); 0 Z 3 0 xe ¡ x dx 3 e 12. g 0 ( e ) = 1 + 2 e ; g is increasing on (0 ; 1 ); g is never decreasing 13. (a) 35; (b) ¡ 24; (c) 28 sq. units
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14. Z 3 0 p 1 + x 2 dx 15. 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 16. 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 ¡ 1 4 1 : 3258 17. (a) 1 2 + 3 ; (b) 15 18. v ( t ) = 1 2 e 2 t + 5 2 in meters/sec; s ( t ) = 1 4 e 2
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Unformatted text preview: t + 5 2 t + 7 4 in meters 19. 80 ft/s 20. Dimensions: x =550 ft y = 2200 3 ft 21. ( ¬° 4 ; 2), (4 ; 2) 22. Assume the base of the triangle is a leg, not the hypotenuse with point ( x;y ) in the Ô¨ārst quadrant; x = 1, y = p 3, A = 3 p 3 2 23. Dimensions: x =5 ft and y =10 ft 24. relative maximum: f ( ¬° 2) = 0, relative minimum: f (0) = ¬° 2 2 3 , vertical tangent line and in¬Īection point at (1 ; 0) 25. relative minimum: f ( ¬° p 3) = 3 p 3 2 and relative maximum: f ( p 3) = ¬° 3 p 3 2 ; in¬Īection point (0 ; 0) 26. a) graph has a hole at (0 ; 0), x-intercept 1, minimum at x = e ¬° 1 = 2 and in¬Īection point ( e ¬° 3 = 2 ; ¬° 3 2 e 3 ) 27. graph has a minimum at x = ¬° 1 and at x = 2 (cusp), and a maximum at x = 1 in¬Īection points at x = 0 and x = 3...
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review4answers11 - t 5 2 t 7 4 in meters 19 80 ft/s 20...

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