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4 Pages

### Ch3-3WS

Course: CALCULUS 0064, Fall 2010
School: Broward College
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Word Count: 261

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Waldron Ch Mrs. 3.3 BC Calculus 604 Rules of Differentiation 1. Given M = at 3 - c 2 t + 2. t dM dM , find a) and b) a dt dA x2 + 3 Find an equation for the tangent line to f(x) = at x = 2, and 2x also for the line perpendicular to the graph at x = 2. #3-4: Find f '(x) 3. f (x) = (x 2 - 1)(x + 21) 4. f (x) = (4x 2 + 1)(2x 4 - 2) 5. Find an equation for the line tangent to the curve y = x2 - 1 at the 3x...

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Waldron Ch Mrs. 3.3 BC Calculus 604 Rules of Differentiation 1. Given M = at 3 - c 2 t + 2. t dM dM , find a) and b) a dt dA x2 + 3 Find an equation for the tangent line to f(x) = at x = 2, and 2x also for the line perpendicular to the graph at x = 2. #3-4: Find f '(x) 3. f (x) = (x 2 - 1)(x + 21) 4. f (x) = (4x 2 + 1)(2x 4 - 2) 5. Find an equation for the line tangent to the curve y = x2 - 1 at the 3x point (1,0). Support your answer graphically. 6. The volume V of a sphere of radius r is 4 r 3 . Notice that 3 dV = A . Explain in terms of geometry why the instantaneous rate of dr change of the volume with respect to the radius should equal the surface area. 7. Find the derivative eighth of f (x) = x 7 + 5x 5 - 4x 3 + 6x - 7 . Think ahead! (the nth derivative, f(n)(x), is the result of differentiating f(x) n times). Find the seventh derivative of f(x). 8. Find f '(x) if f (x) = x2 - 1 x2 + 1 9. Find f '(x) if f (x) = 2x x+3 a 2 -R dC dC b 10. Find and if C = dR dT nT #11-12 Find f '(x) 11. f (x) = (1 - x) (1 + x 2 ) 12. f (x) = (x + 1) (x + 2) (x - 1) (x - 2) 1 13. Suppose that u and v are differentiable functions of x at x = 2 and u(2) = 3, u '(2) = -4, v(2) = 1 and v '(2) = 2. Find the following derivatives: a) d v dx u b) d ( 3u - 2v + 2uv ) dx 14. Find the tangent to the Witch of Agnesi, y = (2,1). 8 at the point 4 + x2
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Broward College - CALCULUS - 0064
Mrs. WaldronCh 3-5 WorksheetBC Calculus1. A weight hanging from a spring is stretched 5 units beyond its restposition (s = 0) and released at time t = 0 to bob up and down. Itsposition at any time t is:s(t) = 5 cos tWhat are its velocity and accele
Broward College - CALCULUS - 0064
Mrs. WaldronCh 3.6BC Calculus 604Chain Rule Worksheet5xy=b)(3x +4) 231. a) x(t) = (3t -2) (t-6)2. Find the derivatives of each of the following, given the table below.xf(x)g(x)f '(x)g '(x)2821/3-333-425a) f(x)/g(x) at x = 2b)f(g
Broward College - CALCULUS - 0064
Mrs. WaldronCh 3.7BC Calculus 604Implicit Differentiation WS1. Find the slope of the circle x2 + y2 = 25 at the point (3,-4)1) Solve for y2) Implicitly2. Show that the slope dy/dx is defined at every point on the graphof 2y = x2 + sin y.3. Find t
Broward College - CALCULUS - 0064
Mrs. WaldronBC Calculus 604Ch 3.8Derivatives of Inverse Trigonometric Functions WS1. Find the derivative:-1( 1x)b) y = sin-1(t )d) y = sec-1(x 2)f) y = cota) y = cosc) y = tane) y = csc2-1(1 - t )-1( 5x )-1( 1 x ) - tan-1(x)2. Us
Broward College - CALCULUS - 0064
Mrs. WaldronBC Calculus 604Ch 3.9 Derivatives of Exponential and Logarithmic Functions1. The spread of a flu in a certain school is modeled by the equation:2001 +e5-tWhere P(t) is the total number of students infected t days after theflue first sta
Broward College - CALCULUS - 0064
Mrs. WaldronCh 4.1BC CalculusAbsolute and Relative Extrema11. Find extreme values of f(x) =4 x25 2x 2 , x 12. Find extreme values of f (x) = x + 2,3. Find extreme values of f (x) = lnx1 + x2x &gt;14. Find extreme values off (x) = lnx1 + x2
Broward College - CALCULUS - 0064
Mrs. WaldronCh 4.2BC CalculusMean Value Theorem1. Find exact solutions to the inequality:a) 2x2 6 &lt; 0b) 3x2 6 &gt; 02. Find the local extrema, the intervals on which the function is increasing andthe intervals on which the function is decreasing:f (
Broward College - CALCULUS - 0064
Broward College - CALCULUS - 0064
Mrs. WaldronCh 4.4BC CalculusModeling &amp; Optimization WSSteps to Solve an Optimization Problem:1. Draw &amp; label a picture2. Create a variable(s) that represent the value to be found3. Write a function in terms of the principal variable by substitutin
Broward College - CALCULUS - 0064
Ms. WaldronCh 4.6BC CalculusRelated Rates Worksheet1. The radius r and surface area S of a sphere are related by the equationS = 4 r2 .Write an equation that relatesdSdrto.dtdt2. When a circular plate of metal is heated in an oven, its radius
Broward College - CALCULUS - 0064
Mrs. WaldronCh 5.1BC CalculusEstimating Area with Finite SumsEx 1: A bug begins to crawl up a vertical wire at time t = 0. The velocity v (ininches/sec) of the bug at time t (in seconds), for 0 t 8, is given by the functionwhose graph is shown below
Broward College - CALCULUS - 0064
Mrs. WaldronCh 5.2BC CalculusWorksheet
Broward College - CALCULUS - 0064
Mrs. WaldronCh 5.3BC CalculusWorksheetFind the position functions, given the following velocity functions.Well start out easy1.v (t) = cos t2.v (t) = sin t3.v (t) = 124.v (t) = 2t + 35.v (t) = 6t + 56.v (t) = t 37.v(t) = 3t 3 - sec 2 t
Broward College - CALCULUS - 0064
Mrs. WaldronAn Introduction to Slope Fields and Differential Equations1.BC CalculusFor each differential equation below:i.Graph the slope field at the points indicated on the grids.ii.Suppose you know that the point (1, 2) is on the graph of f(x)
Broward College - CALCULUS - 0064
Mrs. WaldronCh 6.2BC CalculusIntegration by SubstitutionEvaluate the indefinite integral:1dx1. sec x2. ( csce2u3. u due4.1 + t2x + 3x 2 ) dx32Use substitution to evaluate the integral:5.6. 2t7.x1 - 4x 2dx1 + t 2 dt cos (7t + 5
Broward College - CALCULUS - 0064
Mrs. WaldronCh 6.3BC CalculusIntegration by PartsUse the formula u dv = u i v - v duEvaluate the indefinite integral:ln x1. 2 dxx2. ln ( x23. tanr dr4.3x x e dx5.x1+ 1) dx22cos 2x dx6. sin ( ln t ) dt7. ( ln x )8.x9.x e10.
Broward College - CALCULUS - 0064
Mrs. WaldronCh 6.4Exponential Growth and DecayBC CalculusUse separation of variables to solve the initial value problem.Indicate the domain over which the solution is valid.1.dy= yx and y = 2 when x = 0dx2.dy= t e y and y = 0 when t = 1dt3.
Broward College - CALCULUS - 0064
Ms. WaldronCh 7.1Integral as Net ChangeHw: Pg. 386: 5, 7, 9, 10, 19, 23, 29, 31-36BC CalculusActivity:In exercises 1 and 2, the function v(t) is the velocity in m/sec of a particle movingalong the x-axis and starting at the position s(0) = 8. Use a
Broward College - CALCULUS - 0064
Mrs. WaldronCh 7.2BC CalculusAreas in the Plane WorksheetFind the area of the region enclosed by the two curves f(x) and g(x):1. f(x) = -3x2 + 5 and g(x) = 2x.2. f(x) = 4 x2 and g(x) = x2 43. f(x) = 2x and g(x) = 2x4. f(x) = sin x and g(x) = 3 sin
Broward College - CALCULUS - 0064
Ms. WaldronCh 7.3Volumes Using WashersHw: Ch 7.3: 29, 30, 31BC CalculusIn exercises 1-6 the region in the first quadrant enclosed by the y-axis and thegraphs of f(x) and g(x) is revolved about the x-axis to form a solid. Find itsvolume.1. f(x) = 6
Broward College - CALCULUS - 0064
Mrs. WaldronCh 7.3Volumes Using Cylindrical ShellsHw: Ch 7.3: 33, 34, 42, 63-68BC Calculus1. Find the volume of the solid formed by revolving the region bounded byy = x x3, and the x-axis around the y-axis.2. Find the volume of the solid formed by
Broward College - CALCULUS - 0064
Mrs. WaldronCh 7.4BC CalculusLengths of Curves WorksheetFind the length of each curve on the interval indicated.1. y = 2 sin x from x = 0 to x = 22. y = x 3 from x = 0 to x = 23. y =x - 3 from x = 3 to x = 104. y = e3x from x = 0 to x = 15. y =
Broward College - CALCULUS - 0064
Mrs. WaldronCh 8.1Sequences WorksheetHW: Pg. 441: 1-21 odd, 31-47 oddBC CalculusGiven b1 and bn, find the first three terms and the seventh term for eachsequence.1. b1 = 5, bn = bn-1 5 for all n 22. b1 = 2, bn = 2(bn-1 1) for all n 23. b1 = 11, b
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
Broward College - CALCULUS - 0064
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
Broward College - CALCULUS - 0064
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
Broward College - CALCULUS - 0064
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
Broward College - CALCULUS - 0064
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
Broward College - CALCULUS - 1103
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
Broward College - CALCULUS - 1103
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
Broward College - CALCULUS - 1103
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
Broward College - CALCULUS - 1103
9.2: Taylor SeriesBrook Taylor was an accomplished musician and painter. He did research in a variety of areas, but is most famous for his development of ideas regarding infinite series.Brook Taylor 1685 - 1731Greg Kelly, Hanford High School, Richland,
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
Broward College - CALCULUS - 1103
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
Broward College - CALCULUS - 1103
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
Broward College - CALCULUS - 1103
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
Broward College - CALCULUS - 1103
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
Broward College - CALCULUS - 1103
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
Broward College - CALCULUS - 1103
10.3 day 2Calculus ofPolar CurvesLady Bird Johnson Grove,Redwood National Park, CaliforniaPhoto by Vickie Kelly, 2007Greg Kelly, Hanford High School, Richland, WashingtonTry graphing thison the TI-89.r = 2sin ( 2.15 )0 16To find the slope of a
Broward College - CALCULUS - 1103
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
Broward College - CALCULUS - 1103
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
Broward College - CALCULUS - 1103
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
Broward College - CALCULUS - 1103
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
Broward College - CALCULUS - 1103
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
Broward College - CALCULUS - 1103
A.P. Calculus Formulas 2008-2009Hanford High School, Richland, Washington revised 8/25/08 1. 2. floor function (def) x (graph) Greatest integer that is less than or equal to x.3.ceiling function (def) Least integer that is greater than or equal to x.
Broward College - CALCULUS - 1103
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
Michigan State University - EC 340 - 340
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