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### Ch8-1WS

Course: CALCULUS 0064, Fall 2010
School: Broward College
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Word Count: 150

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Waldron Ch Mrs. 8.1 Sequences Worksheet HW: Pg. 441: 1-21 odd, 31-47 odd BC Calculus Given b1 and bn, find the first three terms and the seventh term for each sequence. 1. b1 = 5, bn = bn-1 5 for all n 2 2. b1 = 2, bn = 2(bn-1 1) for all n 2 3. b1 = 11, bn = 2(bn-1 1) for all n 2 4. b1 = -4, bn = 3bn-1 for all n 2 For each geometric sequence, find a) the common ratio, b) the eighth term, c) a...

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Waldron Ch Mrs. 8.1 Sequences Worksheet HW: Pg. 441: 1-21 odd, 31-47 odd BC Calculus Given b1 and bn, find the first three terms and the seventh term for each sequence. 1. b1 = 5, bn = bn-1 5 for all n 2 2. b1 = 2, bn = 2(bn-1 1) for all n 2 3. b1 = 11, bn = 2(bn-1 1) for all n 2 4. b1 = -4, bn = 3bn-1 for all n 2 For each geometric sequence, find a) the common ratio, b) the eighth term, c) a recursive rule for the nth term, and d) an explicit rule the for nth term. 5. 1, 5, 25, 125, 6. 73, 77, 711, 715, 7. -3, 9, -27, 81, 8. 55-5, 55-15, 55-25, 55-35, Determine whether the given sequence converges or diverges. If it converges, find its limit. 9. a n = -5n + 7 -7 n 10. a n = -3n 2 + 3 2n 2 + 10n + 4 11. a n = n-7 -11 n Use the Sandwich Theorem to show that the sequence converges and then find its limit. n! 12. (2n)! 1 13. 3n sin n 1 14. n - n cos n cos 4n 15. ln n
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Broward College - CALCULUS - 0064
Mrs. WaldronCh 8.2LHpitals Rule WorksheetHw: Pg. 450: 1-11 odd, 14-28 even, 62-67In exercise 1-4, evaluate each limit.1. limx 03. limx 016 + x - 4 - x6x82x+9 -3- x-x2. limx 424. lim BC Calculussin x - cos xx- 4-sin Identify the in
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Mrs. WaldronCh 8.4Improper Integrals WorksheetHw 1: Pg. 467: 4-28 Even,Hw 2: Pg. 468: 31-37 odd, 48-53, 55Evaluate each integral or state that it diverges.1.02.04 dxx + 11x + 30211 dxx + 3x + 223. xe-5xdx14. -8x e-8xdx195.0dx
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Mrs. WaldronBC CalculusCh 8 Review [No Calculator]1. What is the first term of an arithmetic sequence with 100th term 25 andcommon difference 0.2?2. What is the common ratio of a geometric sequence with 10th term2357.947691 and 1st term 1000?3. Use
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Date: _Name: _Math 604 Practice Problems for Chapter 9 Exam! n + 2 \$n1. The sequence cfw_an , where an = #&amp; converges to what value?&quot;n%2.Which of the following series converge? (Circle one)( ! &quot; )e\$nn =1#a.b.&quot;!1001# (! 1000 )nd.(!1)n
Broward College - CALCULUS - 0064
Ms. WaldronCh 9 ReviewBC CalculusPart 1: Convergence and Divergence of Series1. Determine if the following series converges or diverges. Explain yourreasoning. If the series converges give the converged value.n =1enn2. Determine if the following
Broward College - CALCULUS - 0064
Date:_Name:_Math 604 Chapter 7 Practice Exam1. Use the region S bounded by the positive x-axis, the positive y-axis and the curvey = cos x to answer each of the following questions.1y=cos(x)0.5S12a) Compute the area of region S.b) Compute the
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Math 604 Sample Questions from Chapter 51.Use RRAM4 to approximate the definite integral (3 + x )dx7212. Express the limit of the Riemann sum as a definite integralnlim| P | 011+ ck =12kx k where P is a partition of [-3,2]3. Evaluate the
Broward College - CALCULUS - 0064
Ms. WaldronBC CalculusSerious Series Free Response Questions1987 - BC 4a) Find the first five terms in the Taylor series about x = 0 for f(x) =1.1 - 2xb) Find the interval of convergence for the series in part (a).c) Use partial fractions and the
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8.4 day 2Tests for ConvergenceRiverfront Park, Spokane, WAGreg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2006Review:1dx P xP&gt;0(P is a constant.)b 1 lim b P + 1 P +1 P +1 P +11xPdxb P +1 gets bigger If P 1 then
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Ch.8 Extra Topic: Trigonometric SubstitutionsMonticello (Thomas Jeffersons home), Alexandria, VAPhoto by Vickie Kelly, 2004 Greg Kelly, Hanford High School, Richland, WashingtonWe can use right triangles and the pythagorean theorem to simplify some pro
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9.1 9.1 Power SeriesPhoto by Vickie Kelly, 2003Greg Kelly, Hanford High School, Richland, WashingtonStart with a square one Start unit by one unit: unit111111 + + + + + + = 1 2 4 8 16 32 64This is an example of an infinite series. infinite1 21 8 1
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Broward College - CALCULUS - 1103
9.2 day 2 Finding Common Maclaurin SeriesLiberty Bell, Philadelphia, PAPhoto by Vickie Kelly, 2003 Greg Kelly, Hanford High School, Richland, WashingtonThere are some Maclaurin series that occur often enough that they should be memorized. They are on y
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9.3 Taylors Theorem: Error Analysis for SeriesTacoma Narrows Bridge: November 7, 1940Greg Kelly, Hanford High School, Richland, WashingtonTaylor series are used to estimate the value of functions (at least theoretically - now days we can usually use th
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9.4Radius of ConvergencePhoto by Vickie Kelly, 2008Abraham Lincolns Home Springfield, IllinoisGreg Kelly, Hanford High School, Richland, WashingtonConvergence The series that are of the most interest to us are those that converge. Today we will consi
Broward College - CALCULUS - 1103
9.5Testing Convergence at EndpointsPetrified Forest National Park, ArizonaPhoto by Vickie Kelly, 2007 Greg Kelly, Hanford High School, Richland, WashingtonRemember:The Ratio Test:an +1 =L If an is a series with positive terms and lim n a nthen: The
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10.1 Parametric functionsPhoto by Vickie Kelly, 2008Mark Twains Boyhood Home Hannibal, MissouriGreg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2008Mark Twains Home Hartford, ConnecticutGreg Kelly, Hanford High School, Ric
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10.2 day 1: Vectors in the PlaneMesa Verde National Park, ColoradoPhoto by Vickie Kelly, 2003 Greg Kelly, Hanford High School, Richland, WashingtonWarning: Only some of this is review.Quantities that we measure that have magnitude but not direction ar
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10.3 day 1Polar CoordinatesGreg Kelly, Hanford High School, Richland, WashingtonOne way to give someone directions is to tell them togo three blocks East and five blocks South.Another way to give directions is to point and say Go ahalf mile in that
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Hyperbolic FunctionsScottys Castle, Death Valley, CAPhoto by Vickie Kelly, 2005 Greg Kelly, Hanford High School, Richland, WashingtonConsider the following two functions:e e y= 2xxe +e y= 2xxThese functions show up frequently enough that they ha
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Applications of Hyperbolic FunctionsGreg Kelly, Hanford High School, Richland, WashingtonA hanging cable makes a shape called a catenary.x y ven + a cosh E = b though it looks a like a parabola, it is nota some constant a) (for parabola!dy x = sinh d
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Greg Kelly, Hanford High School, Richland, WashingtonThe functions that we have studied this year have allbeen functions of one independent variable:eg:f ( x ) = x2f ( x ) = sin ( x )In real life, functions often have more than oneindependent varia
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z10010An Introduction to Partial Derivativesyx10Greg Kelly, Hanford High School, Richland, Washingtonz100When we have functions with more than one variable, we can find partial derivatives by holding all the variables but one constant.f ( x, y
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Double IntegrationGreg Kelly, Hanford High School, Richland, Washingtonf ( x, y ) = 4 x yFind the volume under this surface between 0&lt;x&lt;2 and 0&lt;y&lt;1.f ( x, y ) = 4 x yz0 &lt; x &lt; 2 and 0 &lt; y &lt; 1We can sketch the graph by putting in the corners where (x
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Hyperbolic FunctionsHyperbolic cosine of x: Hyperbolic sine of x: cosh x =sinh x =e +e 2x xIntegralse x e x 2 sinh u du = cosh u + C cosh u du = sinh u + C sech u du = tanh u + C2 csch u du = coth u + C sech u tanh u du = sech u + C csch u coth u
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