CALCULUS 2 FEBRUARY 2017 # Day Date Assignment Description 91 M 1/30 p. 671 #1, 3, 4, 8, 10, 11, 13, 19, 24 Do part a only for all problems

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1 # Day Date Assignment Description 91 M 1/30 p. 671 #1, 3, 4, 8, 10, 11, 13, 19, 24 Do part a only for all problems Interval of convergence and radius of convergence for 92 Tu 1/31 p. 677 #1, 7, 9, 11, 13, 20, 27 Include the general term for problem #27 only power series Taylor and Maclaurin Series for given functions 93 W 2/1 Worksheet #26 Taylor series and Maclaurin series 94 Th 2/2 p. 671 #41ab, 42abc (don't do the multiplication for part c) and p.677 #10, 12, 14 Derivatives and integrals using power series 95 F 2/3 p. 697 #33, 37, 41 and p. 686 #2, 5, 7 More integration using power series 96 M 2/6 p #41a, 46a, 58, 64, 65, 66, 78 Review 97 Tu 2/7 Worksheet #27 Review for test (AMC Test Periods 1 2 for those on the list) 98 W 2/8 Worksheet #28 Review for test 99 Th 2/9 TEST TODAY!!! Do: Worksheet #29 Test and Review 100 F 2/10 p #1, 2, 4, 6, 9, 12, 39, 45a Rally Schedule Linearization 101 p #3, 5, 8, 11, 35, 38, 43, 46 Note: For 35 and 38, find dy (the estimated change in y) and y (the estimated value of f() AND the following problem: Noting that the point (1,2) satisfies the equation 2 y y 2 + 2y = 2, find an approimate value of y so that (1.01, y) is also on the curve (satisfies the same equation). Review linear and using differentials Print off the BC Calculus Slope Fields Worksheet and bring to class with you tomorrow!!!! 108 Worksheet: BC Calculus Slope Fields Worksheet ***Bring Worksheet to class today NO phones!!*** *******Write directly on the worksheet******** 110 p.545 #3, 7, p. 551-top #125 - show both the slope field and appro. using Euler's method AND THE FOLLOWING 2 problems: 1. Using the local linearization of f() = 9 + sin (2) near 0, an estimate of f(0.06) is A) 0.02 B) 2.98 C) 3.01 D) 3.02 E) Air is escaping from a balloon at a rate of R(t) = 1 + t 2 ft 3 /min, where t is measured in minutes. How much (in ft 3 ) escapes during the first minute? A) 15 B) 15π C) 30 D) 30π E) 30 ln 2 Slope fields Learning to solve differential equations numerically using Euler's method

2 111 p. 545 #5, 8 p.551 #127: show both the slope field and appro. using Euler's method AND THE FOLLOWING 3 Problems: 1) Find the area bounded by the spiral r = ln on the interval π 2π. A) B) C) D) E) ) Find the slope of the curve defined parametrically by = e t, y = t t3 9 at its smallest -intercept. A) B) 2 C) D) E) 1 Learning to solve differential equations numerically using Euler's method. 3) d A) ln 2 ( 3) + C B) ln 2 ( 3) + C C) ln 3 + C D) ln C E) none of these 112 Worksheet #33 Logistic growth problems 113 Worksheet #34 Logistic & Eponential growth 114 Th 2/23 Worksheet #35 Review F 2/24 No School Staff Development Day 115 M 2/27 Worksheet #36 Review 116 Tu 2/28 Worksheet #37 Review LATE START W 3/1 TEST TODAY!! Test Th 3/2 AP Movie F 3/3 AP Movie ANSWERS Assignment #91 1) 1, 1<<1 3) 1/4, 1/2<<0 4) 1/3, 1/3 <1 8) 1, 3< 1 10) 1, 0 <2 11), conv for all 13), conv for all 19) 3, 3<<3 24) 0, conv for =4 only

3 Assignment #92 1) P 3 = ( 1) 1 2 ( 1) ( 1) 3 11) ) P 3 = 2 + 3( 4) 3 3!2 8 13) ! 27. e 2 + e 2 ( 2) + e2 2! ( 2) 2 + e2 3! ( - 2) ( 4) ( 4) ! !... 9) ! 3 3! ) Assignment #94 41a) cos = 1 2 2! + 4 4! 6 6! + 8 8! 10 10! +... conv for all. 41b) ! !... 41c) ! ! 42b) same as problem ! a) same as problem 42c) 2! 3! 4! 5! 10) ! ! ) ) ! !... Assignment #95 33) ) ) error < ! ) ! ! ) 1 2! + 2 4! 3 6! ) ! + 4 3! + 5 4! +... Assignment #96 41a) roc = 3, ioc: 7 < 1; 64) ( 1) n 2n n! n=o 78) a) roc = 1, ioc: 1 < 1; ( + 1) 65) ! 9( + 1) ! 3( + 1) ! + 58) = ( 1) n 3n when 3 < 1 n=o 66) 1 + ( 2) ( 2) 2 + ( 2) 3...

4 Assignment #100 1) L = 4 3 2) L = 1/ ) L = ) L = 4/5 + 9/5 9) L = 5, L(.9) = 5, 12) L = ) dv = 4πr 2 o dr 45). da = 2πr dr = 4 2π(2)(.02) f(.9)= 4.98 L(1.3)=0.575 f(1.3)= =.08π m 2 Assignment # L = L = 1/ L = 2 L(.6) = L = L(8.5) = f(8.5) = dy =.2 y dy=1.0 y dv = 2πr o h dr 46. C = 2πr, dc = 2 in and dc = 2π dr so dr = 1/π so the diameter grew about 2/π in. A = πr 2 and da = 3. for o = 1: for o = 1: πrdr = 2π(5)(1/π) = 10 in 2 Assignment #110 3) y 1 = 4.2, y 2 = 6.216, y 3 = ; eact = ) y 1 = 1.2, y 2 = 1.44, y 3 = 1.728, y 4 = , y 5 = ; eact = e or ) y 5 =.4; eact = ½

5 EXTRA CREDIT Etra Credit is due at the BEGINNING OF THE PERIOD, on a SEPARATE PAPER. Make sure to include the full heading: NAME, DATE, PERIOD, ROW-SEAT, EC #. Show ALL work, SIGN INTEGRITY. You may NOT receive any help from ANYONE or ANYTHING. NO late work accepted for any reason. 0 points will be awarded for not following above directions. 91 For which positive integer n does n 2? 92 In a sequence whose first term is 11, each succeeding term is the sum of the digits of the square of the previous terms. For eample, the second term is = 4 and the third term is 1+6 = 7. What is the 2008 th term of this sequence? 93 If N is the product of three different primes, then its least possible value is If N < 100, what is N s largest possible value? 94 If 26 people (whose first names each start with a different letter) line up at random to climb a ladder, what is the probability that Pat is lucky enough to stand net to Dale? 95 Two sides of a triangle have lengths 5 and 13. The median to the third side has length. What are all possible integral values of? 96 For how many real numbers does 3 6 3? 97 Triangle T s vertices are at (0,0), (5,0), and (1,2). What is the slope of the line through (0,0) that divides T into two triangles of equal area? 98 In the sequence below, each angle is in radians. What is the largest number of consecutive terms of this sequence that can be positive? 99 cos,cos( 1),cos( 2),cos( 3),cos( 4),cos( 5),cos( 6) If a, b, and c are positive integers, what is the largest value less than 1 represented by 1 1 1? a b c 100 Bricklayers Pat and Lee alternate turns in a game in which each player removes from 1 to 100 bricks from a common pile that initially has 2008 bricks. The player taking the last brick wins. If Pat and Lee both play perfectly, and if Pat goes first, then how many bricks must Pat take on his first turn to guarantee a win? 101 Solve for : The First National Bank of Pythagoras was offering a special compounding rate for all new customers. Suppose Elliot has $1000 and invests in an account that pays 50% interest compounded annually. How much money does he have at the end of 2 years? 110 An equilateral triangle is inscribed in a circle of diameter 2. Another circle is then inscribed in the triangle and then an equilateral triangle is inscribed into that circle. If this process continues infinitely, what is the total area of the triangles? 111 A cell phone plan costs $20 each month, plus 5 cents per tet message sent, plus 10 cents for each minute used over 30 hours. In January Michelle sent 100 tet messages and talked for 30.5 hours. How much did she have to pay? 112 The line y = 3 + k is tangent to the curve y = 3 when k is equal to? 113 Last summer 30% of the birds living on Town Lake were geese, 25% were swans, 10% were herons, and 35% were ducks. What percent of the birds that were not swans were geese? 114 The area, in square inches, of the surface of a zone cut from a sphere of radius 4 in. by two parallel planes, one through the center of the sphere and the other 1 in. away, is equal to? 115 In the eight-term sequence A, B, C, D, E, F, G, H, the value of C is 5 and the sum of any three consecutive terms is 30. What is A + H? 116 none

a) rectangles whose height is the right-hand endpoint b) rectangles whose height is the left-hand endpoint

a) rectangles whose height is the right-hand endpoint b) rectangles whose height is the left-hand endpoint CALCULUS OCTOBER 7 # Day Date Assignment Description 6 M / p. - #,, 8,, 9abc, abc. For problems 9 and, graph the function and approximate the integral using the left-hand endpoints, right-hand endpoints,