MATH Calculus of One Variable, Part I Spring 2019 Textbook: Calculus. Early Transcendentals. by Briggs, Cochran, Gillett, Schulz.

Transcription

1 MATH Calculus of One Variable, Part I Spring 2019 Textbook: Calculus. Early Transcendentals. by Briggs, Cochran, Gillett, Schulz. 3 rd Edition Testable Skills Unit 3 Important Students should expect test questions that require a synthesis of these skills. Section 4.1: Maxima and Minima Problems Assigned: 5,9,11,14,15,(2.6.30),17,19,23,31,33,35,41,43,49,52,(2.6.63),53,55,63, 65,75,(3.9.30),77,(3.5.37),78,85,87,89 Answer conceptual questions involving maxima and minima. 5, 9, 77, 78, 89 Use a graph to identify absolute and/or local extrema. 11, 14, 15, Sketch the graph of a function on an interval satisfying given properties. 19 Locate critical points of functions. 23, 31, 33, 35, 41 Determine the existence, location, and value of absolute extrema on a given interval of a function. 43, 49, 52, 53, 55, 63, 65 Solve applications involving maxima and minima (*Review: Find points of discontinuity or intervals of continuity.) (2.6.30) (*Review: Evaluate limits using continuity principles.) (2.6.63) (*Review: Find derivatives involving logarithms and exponentials.) (3.9.30) (*Review: Find derivatives of products, quotients, and powers of functions with trigonometric expressions.) (3.5.37) Section 4.2: Mean Value Theorem Problems Assigned: 3,5,6,7,8,11,15,18,21,25,26,29,33,36,37,39,49,50 Answer conceptual questions involving Rolle s Theorem and the Mean Value 3, 8, 33 5, 6, 7 Theorem. Determine if Rolle s Theorem applies and find the point(s) guaranteed to 11, 15, 18 exist by Rolle s Theorem. Find the point(s) guaranteed to exist by the Mean Value Theorem. 21, 25, 26, 29 Find functions with the same derivative of a given function. 36, 37, 49 Use graphs to answer questions involving the Mean Value Theorem. 39 Solve applications involving the Mean Value Theorem. 50

2 Section 4.3: What Derivatives Tell Us Problems Assigned: 6,7,9,11,17,19,25,29,31,34,40,46,47,51,54,57,59,61,63,67,73,77,83,87,90,96,99,105,107 Answer conceptual questions involving derivatives. 7, 9, 11, 17, Find the intervals on which a function is increasing or decreasing. 19, 25, 29, 31, 34, 40 Use the first derivative test to locate critical points and local and absolute 46, 47, 51, extrema. Sketch the graph of a function given properties of the function. 59, 61, 105 Determine the concavity on intervals and find inflection points. 63, 67, 73 Determine if critical points correspond to local maxima/minima using the 77, 83, 87, 90 second derivative test. Compare the graphs of a function with the graphs of its first and second derivatives. 96, 99 Section 4.4: Graphing Functions Problems Assigned: 3,8,11,15,25,29,33,35,37,42,45,47,55,56,57 Answer conceptual questions about graphing functions. 3, 8, 11, 55 Graph functions using analytic methods involving derivatives. 15, 25, 29, 33, 45 35, 37, 42 Graph a function given the graphs of its first and/or second derivatives. 47 Use the derivative of a function to sketch a possible graph of the function. 56, 57 Section 4.5: Optimization Problems Problems Assigned: 4,7,13,15,16,17,21,22,(3.9.27),25,27,31,33,37,40,49,57 Answer conceptual questions involving optimization. 4 Optimize the sum, product, or sum of squares of two number given 7, 15 constraints. Solve optimization problems involving geometry or algebraically defined 13, 17, 22, 25 curves. Solve applications involving optimization. 16, 21, 27, 31, 33, 37, 40, 49, 57 (*Review: Find derivatives involving logarithms and exponentials.) (3.9.27)

3 Section 4.6: Linear Approximation and Differentials Problems Assigned: 2,3,10,15,25,29,30,33,(3.4.29),38,39,41,43,48,50,(3.4.37),52,55,56,59,61,64,67,69,71 Answer conceptual questions involving linear approximation and 2, 3, differentials. Find a linear approximation function. 15 Write a linear approximation function, and estimate the value of a function 25, 29, 30, 33 and evaluate the error. Choose a value to minimize error and use it to write a linear approximation 38, 39, 41, 43 of a quantity. Graph a function and its linear approximation to identify overestimates and 48, 50 underestimates. Solve applications involving linear approximations. 52, 55, 56, 59 Given a function, write a differential expression expressing the change in the 61, 64, 67, 69 dependent variable as a function of a change in the independent variable. (*Review: Find derivatives of products and quotients of algebraic (3.4.29) expressions.) (*Review: Find derivatives of products and quotients involving exponentials.) (3.4.37) Section 4.7: L Hôpital s Rule Problems Assigned: 3,7,17,21,22,25,37,39,(3.5.29),41,45,48,52,53,57,61,65,(4.4.17),69,73,75,78,79,81,85, 95,100,103,119 Answer conceptual questions involving L Hôpital s Rule. 3, 7 Evaluate limits using the form 0/0 or infinity/infinity of L Hôpital s Rule, if it applies. 17, 21, 22, 25, 37, 39, 41, 45, 48, 52, 69 Evaluate limits involving the indeterminate form 0*infinity. 53, 57, 73 Evaluate limits involving the indeterminate form infinity infinity. 61, 65 Evaluate limits involving the indeterminate forms 1^infinity, 0^0, and 75, 78, 79, infinity^0. Solve applications involving L Hôpital s Rule. 85 Use limit methods to compare growth rates of functions. 95, 100, 103 (*Review: Find derivatives of products, quotients, and powers of functions (3.5.29) with trigonometric expressions.) (*Review: Graph functions using analytic methods involving derivatives.) (4.4.17)

4 Section 4.9: Antiderivatives Problems Assigned: 4,(3.7.42),9,11,13,17,19,21,22,25,27,34,35,(3.7.49),40,43,57,62,69,73,79,86,87,91,93, 97,107,111,112,114,120 Answer conceptual questions involving antiderivatives. 4, 9, 111, 112, 114, 120 Find all antiderivatives of a function. 11, 13, 17, 19, 21, 22 Determine the indefinite integral of a function. 25, 27, 34, 35, 40, 43, 57, 62 Given a function, find the antiderivative satisfying a given condition. 69, 73 Given the derivative of a function, find the function satisfying an initial 79, 86 value. Graph the solutions to a differential equation, then the particular solution 87 given an initial value. Find a position function given a velocity function and an initial position or an 91, 93, 97 acceleration function and an initial velocity and an initial position. Solve applications involving antiderivatives. 107 (*Review: Find derivatives of basic functions using the chain rule.) (3.7.42) (*Review: Use the chain rule multiple times and use the chain rule with the product and quotient rules.) (3.7.49) Section 5.1: Approximating Areas Under Curves Problems Assigned: 1,7,9,11,13,15,(4.3.40),17,(4.3.47),23,37,41,44,47,49,71,73 Approximate displacement using a specified number of subintervals of a 1, 15, 17 velocity function. Answer conceptual questions involving areas under curves. 7, 13 Illustrate, calculate, and compare left, right, and midpoint Riemann sums. 9, 11, 23, 37, 41 Evaluate Riemann sums from tables. 44 Express given sums in sigma notation or evaluate expressions in sigma 47, 49 notation. Solve applications involving areas under curves. 71, 73 (*Review: Find the intervals on which a function is increasing or decreasing.) (4.3.40) (*Review: Use the first derivative test to locate critical points and local and absolute extrema.) (4.3.47)

5 Section 5.2: Definite Integrals Problems Assigned: 2,14,16,18,28,29,35,37,41,43,45,47,53,55,57,65,79,80,81,83,90 Answer conceptual questions involving definite integrals. 2, 14, 16 Sketch the graph of a curve and approximate the net area using Riemann 18 sums. Use geometry to find area and net area of a described region. 28, 29 Write definite integrals from the limits of sums. 35, 37 Sketch the graph of an integrand and use geometry to evaluate the definite 41, 43, 45, 90 integral. Evaluate definite integrals using properties of definite integrals. 47, 53, 55, 57, 65 Use the limit definition of the definite integral to evaluate definite integrals. 79, 83 80, 81 Section 5.3: Fundamental Theorem of Calculus Problems Assigned: 3,9,13,14,16,19,( ),23,25,33,39,42,46,47,59,64,69,71,75,85,87,94,98,(4.9.45),106,111 Answer conceptual questions involving the Fundamental Theorem of 3, 9 87 Calculus. Given a graph and areas of designated regions, evaluate area functions. 13, 14 Find and verify area functions. 16, 19 Evaluate definite integrals using the Fundamental Theorem of Calculus. 23, 25, 33, 39, 42, 46, 47, 59 Find areas bounded by functions. 64, 69, 71, 106 Evaluate derivatives of definite integrals. 75, 85 Evaluate area functions. 94, 98 Maximize values of definite integrals and solve integral equations. 111 (*Review: Find derivatives of functions involving inverse trigonometric ( ) functions.) (*Review: Determine the indefinite integral of a function.) (4.9.45)