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Teacher sees 3 day weekend coming up, assigns these 3 lovely gifts due after the long weekend. Ahh AP calculus: 1 l 07 Sec 2.1 & 2.2 Worksheet 1 Sec 2.1-2 Limits (Worksheet 3) 1& 2.2 Algebraic Limits (Worksheet 2) 1. For the function f graphed below, find (b) lim f(x) x-3 + 6x3 -16) 2.5.2 Find lim 2. Exercise Set 2.5 (a) lim f(x) z-3 Find lim ( (d) f(3) 2-16 I2r- 20 7-6x5 lim (c) lim f(x) z-3 2.5.4 Find lim Find the limits in Exercises 1-56 x-2 23. lim 43. Find lim 6+ (e) lim f(x) (f) lim f(x). 1. lim 7. 33s7-4s5 lim 5-2r3 lim t 12+1 -2 +2 1 -2 -3 H.A 44. Find lim B1z2 +5x-6 2.5.6 24. Find lim 2. lim (-3) 2s7 ON-22 5. For th VSx2-2 lim 6-13 lim t 7t3+3 2 45. ,2 Find lim a2 (a) 3. lim T -G), x<B 2.5.8 25. Find lim l -4z+3 z-0 x +3 a 57 im (c) 4. lim 3x V5x2-2 46. lim -2 -27 Find lim T3l-3x2 2 2.5.10 26 lim X Find lim 5. lim 12y. x +3 X (e) N 3 y-3 (-e-3) ix-3 47. lim 2-y lim (-2h) h+a 27. lim V7+6y 1 6. h-4h ind lim 2h2 IX-3 2.5.12 Find lim 2. For the function f graphed below, find 1 XCXa} aa) 7. lim Vx3- 3x-1. 48. lim -3 X A-2 (b) lim f(x) HI2 28. lim 2 y -3 (a) lim f(x) z-5 1 y V7+6y2 x-9 lim r-9 Vx-3 8. lim (x4+12x3-17x +2). (d) f(2) 49 k (c) lim f(x) z-2 3+h 3 r-0 V3x1+x lim 2.5.14 Find lim 29. r+ a 9. lim (y 12y +1) x2-8 4-y (e) lim f(x) (f) lim f(x). y-1 50. lim y-42-Vy lim Vx 4 1- V3x +x lim zI3 x2-2x 6. For t d lim I3 -27 10. lim z-3 X+1 30. 2.5.16 Find lim -2 x2-8 51. (a) y=f(x) (y 1(y 2) y +1 2 lim 52. lim V5- x. 11. 31. lim y-2 (c) h-21-2 21-2 x-3' X-3 lim 2.5.18 Find lim r-4 NI4 H 4 12. lim -0x 12x +3 6x-9 53. lim (3 x) (e) 32 lim I-3 X-3 222-1 x2- 16 54 lim (3 x2). 2.5.20 Find lim Ito N +1 13. lim 33. lim x-3 x 3 -1 11 z -4 X-4 3. For the function g graphed below, find 55 lim (12x -3x5). 13+8 lim t-21+ 2 (a) lim g(x) 1-4 (b) 1-4 lim g(x) lim 03x3 + 4x2+5 14. 34 2.5.22 Find lim 56. lim (2x3 100x + 5). lim x-2 x2 4 2x (c) lim g(x) (d) g(4) x 1 lim HI4 15 35 57. Find V3z+ 4z-1 im Foo lim x-2 (e) lim g(x) lim g(x) 2.5.24 Find lim 4 (f) 3- x2-4x + 4 lim xaXta RI1H 16. lim -2 x+x-6 X VIT4NII 3- 36. lim x-2 X2 where a is an arbitrary constant. Hint: Consider the cases, a 0 and a 0 separately.] 4 x2+6x+ 5 lim * 1 X2-3x- 4 7. For 17 37 lim y +6 y=g(x) 31 -6 y 36 (a) d lim f(z) where f() 13+ 12-5t+3 58. Let f(x) = x3-1 18. lim 38. lim y+6 H, HV 3 13-31+2 x1 (c) t-1 y-6 y2-36 (a) Find lim f(x). 3x+1 lim 2r-5 (e) 4 19. y +6 x-1 39. lim (b) Sketch the graph of y f(x) 59. Let HAI lirm f(x) where f(z) y6 y 36 1-2r, r V 20. lim 1 3-x z- X-12 40. lim -4 X-2x-8 -1 xS 3 f(x)= 13x 1 , { 21. lim 3-x 7, x > 3 the right hand limit at r= 1 for f(x) = 6, y yt 4 41 lim Find x-4 x-2x- 8 4. For the function g in the following graph, find (a) 1 + Sx2+7 lim (a) lim f(x) (b) lim f(x) z 3 ar<1 22. 42. lim 1-4 X2-2x--8 3 x x-3 lim g(x) (b) lim g(x) -0+ x -1, (c) lim f(x) he left hand limit at r=0 for f()= x-3 Exercise Set 2.5 (Page 129) (c) lim g(x) (d) g(0) 1. 7 3. 5. 36 43.- 7. V10 45. - (e) lim g(x) 9. 14 47-1 (f) lim g(x). 11.0 r2 1, rA 3 49, 6 51. 53. +oo nf(x) where f(x) 13. 8 15. 4 17. - (r 1)3, 55.- 57.4 if a 0, 1 if a = 0 rV3 19. 21. O 23. 0 59.(a) 2 (b) 2 (c) 2 25. -VS 61, 4 27. 1/V6 33. does not exist 39. does not exist 29. V3 65. 31. +o 67. 35, - 69. 0 37. + 71. 41. + 73. a/2 75. if r(a) is defined Teacher sees 3 day weekend coming up, assigns these 3 lovely gifts due after the long weekend. Ahh AP calculus

Teacher sees 3 day weekend coming up, assigns these 3 lovely gifts due after the long weekend. Ahh AP calculus

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AP Calculus BC: How do you do this??: The AP CALCULUS PROBLEM BOOK 78 Maximize or Minimize? 3.8 a box as part of her science project. It is by 40 cm 743. The famous Kate Lynn Horsefeed is building to be built from a rectangular piece of cardboard measuring 25 cm a square from each corner and then bending up the sides. Find the size of the corner square which will produce a container that will hold the most. bycutting out 744. Ashley is building a window in the shape of an equilateral triangle whose sides each measure 4 meters. Ashley wants to inscribe a rectangular piece of stained glass in the triangle, so that two of the vertices of the rectangle lie on one of the sides of the triangle. Find the dimensions of the rectangle of maximum area that can be inscribed in the given triangle. 745. It has been determined by the brilliant deductive mind of Bruce Wayne that Gotham Highway is located on the line y 2x +3. Determine the point on Gotham Highway closest to the Wayne Foundation Building, which happens to be located at the point (1,2). 746. Vaidehi wants to cut a 30-meter piece of iron into two pieces. One of the pieces will be used to build an equilateral triangle, and the other to build a rectangle whose length is three times its width. Where should Vaidehi cut the iron bar if the combined area of the triangle and the rectangle is to be a minimum? How could the combined area of these two figures be a maximum? Justify your answers. 747) An open oak wood box with a square base is to be constructed using 192 cm2 of oak. If the volume of the box is to be maximized, find its dimensions. 8 8x4cm 748 At the Skywalker moisture farm on the desert planet Tatooine, there are 24 moisture processors, with an average yield per processor of 300 cubits of moisture. Research conducted at Mos Eisley University concludes that when an additional processor is used, the average yield per processor is reduced by 5 cubits. Help Owen and Beru Skywalker find the number of moisture processors that will maximize the number of cubits. 749. The fence around Wayne Manor is going to be replaced. No fence will be required on the side lying along Gotham River. If the new wrought iron fence costs $12 per meter for the side parallel to the river, and $4 per meter for the other two sides, find the dimensions of the maximum area that can be enclosed by the fence if Bruce Wayne cannot spend more than $3600. 750. The Gotham-Metropolis Highway is a toll road that has averaged 54,000 cars per day over the past five years, with a $.50 charge per car. A study conducted by the Ray Chulldel Lavet University concludes that for every S.05 increase in the toll, the number of cars will be reduced by 500. In order to maximize revenue, what toll should the highway charge? 751. The range R of a projectile whose muzzle velocity in meters per second is v, and whose angle of elevation in radians is 0, is given by R gravity. Which angle of elevation gives the maximum range of the projectile? (v2 sin(20))/g where g is the acceleration of 752. A piece of wire 100 cm long is to be cut into several pieces and used to construct the skeleton of a box with a square base. a) What is the largest possible volume that such a box can have? b) What is the largest possible surface area? AP Calculus BC: How do you do this??

AP Calculus BC: How do you do this??

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