AP Calculus AB FIVES Sheet F = Fun at Home, I = Intellectual, V = Variety, E = Endeavors, S = Specimens

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1 AP Calculus AB F heet F = Fun at Home, = ntellectual, = ariety, = ndeavors, = pecimens #62 Monday 11/26 F Worksheet 43 Print Worksheet 44 1) Find c for the Mean alue Theorem for 2) Find c for Rolle s Theorem for Last Problem on Worksheet 41 Related Rates Last Day of Related Rates #63 Tuesday 11/27 F Worksheet 44 None Review for Test Mean alue Theorem and Related Rates #64 Wednesday 11/28 F Worksheet 45 None Review for Test Mean alue Theorem and Related Rates #65 Thursday 11/29 F Worksheet 46 Test Mean alue Theorem and Related Rates #66 Friday 11/30 F Worksheet 47 Print Worksheet f 2. xpress the following situation as a definite integral and evaluate the integral: Find the amount of water lost from a bucket leaking 0.4 liters per hour between 8:30 a.m. and 11:00 a.m. None Approximating Area using Riemann ums For the following function, approximate areas under the curve using four subintervals for left, right, midpoint rectangles and trapezoids. Then find the area using the definite integral. Graph each part (yes, that means you will have 5 graphs). 1) a) Left Rectangular Approximation with graph b) Right Rectangular Approximation with graph c) Midpoint Rectangular Approximation with graph d) Trapezoidal Approximation with graph e) xact Area using definite integrals with graph

2 #67 Monday 12/3 F Worksheet 48 Print Worksheet 49 1), then the value of at 2) The table below gives selected values for f is continuous on the interval, what is the value of? Approximating Area using Riemann ums More examples of Approximating Area using Riemann ums #68 Tuesday 12/4 F Worksheet 49 Print Worksheet 50 1) 2) 3) xpress the following situation as a definite integral and evaluate the integral: Find the output from a pump producing 25 gallons per minute during the first hour of operation. None xact Area under a curve using ntegration x. 1 x. 2 x. 3 x. 4 x. 5 #69 Wednesday 12/5 F Worksheet 50 Print Worksheet 51 2 x 1) ( 4x 2 2)dx = 2) f f ( x) = 1 x 2 + 1, then f ' x x 1 ( ) 2 x dx Area Between two curves about the x-axis ( top minus bottom ) ( ) = (Only simplify the numerator) Find the area of the regions enclosed by the lines and curves. x. 1 x. 2 The region on or above the x-axis bounded by the curves. x. 3 Find the area of the region in the first quadrant bounded by the line, the line, the curve and the x-axis.

3 #70 Thursday 12/6 F Worksheet 51 Print Worksheet 52 sin ( x ) sin π 1) lim 4 x π 4 x π 4 2) f f ( x) = tan 2 ( 8 2x), then f '( 1) = ( ) satisfies the conclusion of the Mean alue Theorem for the function ( ) = 3x 2 + 4x + 1, then. f a number c in the interval 1,2 f x Area Between two curves about the y-axis ( right minus left ) Find the area of the regions enclosed by the lines and curves. x. 1 x. 2 #71 Friday 12/7 F Worksheet 52 Print Worksheet 53 Find an equation of the line tangent to the curve x 2 + y 2 = 16 at the point. valuate Average Y alue and Review x. 1 Find the average value of. x. 2 Find the average value of. #72 Monday 12/10 F Worksheet 53 None Review for Test Riemann ums, xact Areas, Average Y alue #73 Tuesday 12/11 F Worksheet 54 Print Worksheet 55 f then Test Riemann ums, Areas, Average Y alue #74 Wednesday 12/12 F Worksheet 55 Print Worksheet 56 valuate Properties of ntegration; Review We will be discussing some of the basic properties of integration that we can apply to various problems.

4 #75 Thursday 12/13 F Worksheet 56 Print Worksheet A factory produces bicycles at a rate of R(t) = t 2 t bicycles per week (in t weeks). How many bicycles were produced from day 8 to 21? 2. A population of insects increases at a rate of R(t) = t t 2 insects per day. Find the insect population after 3 days, assuming that there are 35 insects at t = 0. None Derivatives and ntegrals using a Calculator - We have not been using the calculator very much this year, but it is important for us to learn how to do the integral and derivative using the calculator. x. 1 Find the slope of the tangent line to the graph of f x ( ) = 3x 2 4x +1 when x = 2. x. 2 Find the equation of the tangent line to the graph of f ( x) = sin x when x = π 3. x. 3 valuate 1 4 ( 2x cos x)dx #76 Friday 12/14 F Worksheet 57 Let f be a differentiable function with and, and let g be the function defined by Product Rule to find.. Find an equation of the line tangent to the graph of g at the point where. Hint: Use the What are all the values of k for which L Hopital s Rule uppose that Then that x. 1 x. 2 #77 Monday 12/17 F Worksheet 58 1) Find the equations of the asymptote(s) for the graph of 2) Find the limit: a. b. 3) A survey shows that a mayoral candidate is gaining votes at a rate of R( t) = 2,000t +1,000 votes per day, where t is the number of days since he announced his candidacy. How many supporters will the candidate have after 60 days, assuming that she had 50 supporters at t = 0? Today you learn how to find volumes of a solid of revolution using DK: Let R be the region enclosed by the graphs of and. Find the volume of the solid generated by revolving the region R about the y-axis.

5 #78 Tuesday 12/18 F Worksheet valuate 2. Water flows into an empty reservoir at a rate R( t) = 3, t gal/hour. What is the quantity of water in the reservoir after 5 hours? valuate without using a calculator. Today you learn how to find volumes of a solid of revolution using WAHR: Let R be the region enclosed by the graphs of and. Find the volume of the solid generated by revolving the region R about the x-axis. #79 Wednesday 12/19 F Worksheet 60 1) Find the average value of over the interval. 2) Find the area between the curves. Find More olumes by Disks and Washers None #80 Thursday 12/20 F Worksheet 61 1) Find 2) Find the value of c that satisfies Rolle s Theorem for Today you learn how to find volumes of solids of revolution where the axis of rotation is neither the x or y axis. Let R be the region enclosed by the graphs of and. Find the volume of the solid generated by revolving the region R about the line. #81 Friday 12/21 F will be posting 1 review Worksheet at the beginning of each week during Christmas break. DO NOT wait until your break is over to complete the Worksheets. TAY HARP!! None njoy your day today! njoy your Christmas Break and Happy New Year!! ee you in 2013!