CALCULUS 2 FIVES SHEET F=Fun at home I=Incunabula V=Variety E=Endeavors S=Specimens Thursday, 12/3

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1 Thursday, 12/3 F #70 (yes, it is strange that this 5 sheet is #70) As shown in the figure above, water is draining from a conical tank with height 12 feet and diameter 8 feet into a cylindrical tank that has a base with area 400π square feet. The depth h, in feet, of the water in the conical tank is changing at the rate of (h 12) feet per minute. The volume V of a cone with radius r and height h is V = 1 3 πr2 h. (a) Write an expression for the volume of water in the conical tank as a function of h. (b) At what rate is the volume of water in the conical tank changing when h = 3? Indicate units of measure. (c) Let y be the depth, in feet, of the water in the cylindrical tank. At what rate is y changing when h = 3? Indicate units of measure. Let f be a function whose domain is the closed interval [0, 5]. The graph of f is shown below. x Consider the function G defined by G(x) = f(t). 0 (a) Find G(3). (b) On what intervals is G increasing and concave down? Show your reasoning. (c) Find an equation of the tangent line to the graph G at the point where x = 3. I 1. The area of the region bounded by y = sin 2x and y = 2 sin x for 0 x π is A) 0 B) 2 C) 4 D) 5 E) 6 2. If f(x) = sin x x 2, then f ' (π) = A) 1 π 2 B) 1 π 2 C) 2 π 2 D) 2 π 3 E) π 2 π 3 V Worksheet #21 (34) E To practice a free response problem like those on the AP test. S BC Free Response (4) 2. p.179 (30)

2 SURPRISE TESTS 1. AP-type exam, usually multiple choice questions because many questions are still unknown to you, a guessing equalizer applies...to keep you from guessing on what you don t know. (minus 1 1/4 for an incorrect answer) there is NO guessing penalty on the actual AP exam. 2. There will be more questions than you can answer in time allotted. There may be problems that we haven't covered yet. Work as quickly as you can doing the easiest problems first. 3. Sometimes with, sometimes without calculators 4. Will count like a normal test if you miss it, you will take the Comprehensive Make-up Exam 5. No homework the night of a Surprise Test. Thus, the 5 sheets are not dated near the time of a surprise test, to keep you surprised! F #66 Worksheet #21 Problems (17,18,19,36,39,43) Show work without a calculator. I Worksheet #21 (14) D S Soon! Very Soon!! F #67 Worksheet #21 Problems (21 26) Show work without a calculator. I Worksheet #21 (13, 15) Make sure that you fully justify your answers. C and B S Soon! Very Soon!! F #68 Worksheet #21 Problems (27,28,29,31,33,35) Show all work without a calculator. I Worksheet #21 (41) D S Some former students say that they wish they would have practiced better study habits during their senior year in high school to give them an edge in college. F #69 Worksheet #21 Problems (2,4,5,8,10,42) Show all work without a calculator. I Worksheet #21 (12) E S Some former students say that they wish they would have practiced better study habits during their senior year in high school to give them an edge in college. Friday, 12/11/15 Winter Sports Rally F Semester 1 Final Prep Worksheet #1

3 Monday, 12/14 F Semester 1 Final Prep Worksheet #2 Tuesday, 12/15 F Semester 1 Final Prep Worksheet #3 Wednesday, Thursday, Friday 12/16, 12/17, 12/18 See Final Exam schedule below THE FINAL EXAM WILL BE AN AP style TEST AND WILL BE WORTH 4000 POINTS. Winter Break Assignment F That's right! Another wonderfully designed *** HOLIDAY ADAGE *** IT'S THE LAST ADAGE OF THE YEAR!!. Be sure that you show all work on your work paper for full credit. The message on this adage could prove to be very valuable to you!! Remember that the adage is designed to be done at the end of winter break so that you come back renewed and refreshed and ready for more exciting CALCULUS! E *** HAPPY HOLIDAYS *** *** I WILL SEE YOU IN JANUARY*** S Be good, have fun, and be careful this holiday!!

4 Fall Semester Final Examination Schedule Wednesday, December 16 0 FINAL 8:01 AM 10:01 AM 3 FINAL 10:16 AM 12:16 PM Lunch 12:16 PM 12:54 PM 6a FINAL 1:00 PM 3:29 PM 6b FINAL 1:00 PM 3:00 PM Thursday, December 17 1a FINAL 7:32 AM 10:01 AM 1b FINAL 8:01 AM 10:01 AM 2 FINAL 10:16 AM 12:16 PM Friday, December 18 4 FINAL 8:01 AM 10:01 AM 5 FINAL 10:16 AM 12:16 PM

5 Assignments #66, 67, 68, 69 Assignment #70 1. (a) (b) (c) CALCULUS 2 FIVES SHEET ANSWERS Answers are on the worksheet. V = 1 3 πr2 r h Since in the cone, h = 4 12 = 1 3, then V = 1 3 π 1 3 h 2 1 h = 27 π h3 dv = 1 dh π h2 substituting h = 3 and dh = h 12 yields 9 dv = 1 9 h2 (h 12) = 1 9 π (9) ( 9) = 9π ft3 /min Rate of decrease in conical tank = rate of increase in cylindrical tank, thus dv = 9π. For cylinder, V = π r 2 y = 400 π y thus dv = 400π dy and this yields 400π dy = 9π so, dy = ft/min 2. 3 (a) G(3) = f(t) 1 (1)(1) 1(1) (b) G inc so G or f + when 0 < x < 2.5 or 4.6 < x < 5 G con down when G or f so G or f dec when 2 < x < 4 Both: when 2 < x < 2.5 (c) x = 3, G(3) = 3/2, G (3) = f(3) = 1 so 2x + 2y 9 = 0 or y 1.5 = 1(x 3) Semester 1 Final Prep Worksheets Answers are on the worksheets.

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