• 96 Pages ch01
    Ch01

    School: Kennesaw

    *(866)487-8889* CONFIRMING PROOFS MASTER SET Please mark all alterations on this set only hof51918_ch01_001_096 9/27/05 3:14 PM Page 1 CHAPTER 1 Supply and demand determine the price of stock and other commodities. FUNCTIONS, GRAPHS, AND LIMITS

  • 102 Pages ch05
    Ch05

    School: Kennesaw

    CHAPTER 5 Computing area under a curve, like the area of the region spanned by the scaffolding under the roller coaster track, is an application of integration. INTEGRATION 1 2 3 4 5 6 Antidifferentiation: The Indefinite Integral Integration by Sub

  • 3 Pages 1.7 Notes
    1.7 Notes

    School: Kennesaw

    Section 1.7: The Chain Rule Section Objectives: Find the composition of two functions. Differentiate using the Extended Power Rule or the Chain Rule. THEOREM 7: The Extended Power Rule Suppose that is a differentiable function of . Then, for any real nu

  • 2 Pages 1.8 Notes
    1.8 Notes

    School: Kennesaw

    Section 1.8: Higher Order Derivatives Section Objectives: Find derivatives of higher order. Given a formula for distance, find velocity and acceleration. Higher Order Derivatives () Consider the function given by . Its derivative, ( ) is given by () . T

  • 4 Pages 2.1 Notes
    2.1 Notes

    School: Kennesaw

    Section 2.1: Using Derivatives to Find Max & Min Values & Sketch Graphs Section Objectives: Find relative extrema of a continuous function using the First-Derivative Test. Sketch graphs of continuous functions. A function is increasing over if, for ever

  • 4 Pages 2.2 Notes
    2.2 Notes

    School: Kennesaw

    Section 2.2: Using Second Derivatives to Find Max & Min Values and Sketch Graphs Section Objectives: Find the relative extrema of a function using the Second-Derivative Test. Sketch the graph of a continuous function. Suppose that is a function whose de

  • 3 Pages 2.3 Notes
    2.3 Notes

    School: Kennesaw

    Sec. 2.3: Graph Sketching: Asymptotes & Rational Functions Section Objectives: Find limits involving infinity. Determine the asymptotes of a functions graph. Graph rational functions. DEFINITION: A rational function is a function that can be described

  • 2 Pages 2.4 Notes
    2.4 Notes

    School: Kennesaw

    Section 2.4: Using Derivatives to Find Absolute Max & Min Section Objectives: Find absolute extrema using Maximum-Minimum Principle 1. Find absolute extrema using Maximum-Minimum Principle 2. DEFINITION: Suppose that is an is an is a function with domai

  • 3 Pages 2.5 Notes
    2.5 Notes

    School: Kennesaw

    Section 2.5: Max-Min Problems; Business & Econ Applications Section Objectives: Solve maximum and minimum problems using calculus. A Strategy for Solving Maximum-Minimum Problems: 1. Read the problem carefully. If relevant, make a drawing. 2. Make a list

  • 3 Pages 2.6 Notes
    2.6 Notes

    School: Kennesaw

    Section 2.6: Marginals and Differentials Section Objectives: Find marginal cost, revenue, and profit. Find and Use differentials for approximations. DEFINITION Let and represent, respectively, the total cost, revenue, and profit from the production and

  • 3 Pages 1.6 Notes
    1.6 Notes

    School: Kennesaw

    Section 1.6: Differentiation Techniques: The Product and Quotient Rules Section Objectives: Differentiate using the Product and the Quotient Rules. Use the Quotient Rule to differentiate the average cost, revenue, and profit functions. THEOREM 5: The Pr

  • 6 Pages math 1106 test 2 answer key-fall 08
    Math 1106 Test 2 Answer Key-fall 08

    School: Kennesaw

    Math 1106 Test 2 fall 08 Answer Key Cross Reference This cross reference will match the question numbers in the answer key to test versions 1 & 2. v.1 v.2 1 2 3 4 5 17 9 12 20 7 15 4 6 7 9 12 13 25 23 24 6 7 8 9 v.1 v.2 11 19 5 13 17 20 16 3 5 v.1

  • 7 Pages math 1106 test 3 answer key-fall 08
    Math 1106 Test 3 Answer Key-fall 08

    School: Kennesaw

    Math 1106 Test 3 fall 08 Answer Key Cross Reference This cross reference will match the question numbers in the answer key to test versions 1 & 2. v.1 v.2 1 2 3 4 5 8 13 19 22 11 17 12 21 2 13 14 10 24 25 23 6 7 8 9 v.1 v.2 7 3 20 10 4 5 15 3 9 v.1 v

  • 7 Pages math 1106 test 3 answer key-spring 09
    Math 1106 Test 3 Answer Key-spring 09

    School: Kennesaw

    Math 1106 Test 3 spring 09 Answer Key Cross Reference This cross reference will match the question numbers in the answer key to test versions 1 & 2. v.1 v.2 1 2 3 4 5 8 9 5 22 1 1 14 12 6 15 2 8 25 24 23 6 7 8 9 v.1 v.2 18 3 13 16 4 19 10 9 21 v.1 v.

  • 6 Pages math 1106 test 4 answer key-spring 09
    Math 1106 Test 4 Answer Key-spring 09

    School: Kennesaw

    MATH 1106 - test 4 key- Spring 2009 Multiple choice answers v.1 v.2 1 2 3 4 5 A A A A A B B B A B A D A A A 6 7 8 9 v.1 v.2 A B B B D D D D A v.1 v.2 11 D 12 D 13 B 14 B 15 C C C C D B v.1 v.2 16 D 17 A 18 D 19 D 20 A D B A A B 10 D v.1 v.2 21

  • 3 Pages 1.5 Notes
    1.5 Notes

    School: Kennesaw

    Section 1.5: Differentiation Techniques: The Power & SumDifference Rules Section Objectives: Differentiate using the Power Rule or the Sum-Difference Rule. Differentiate a constant or a constant times a function. Determine points at which a tangent lin

  • 3 Pages 1.1 Notes
    1.1 Notes

    School: Kennesaw

    Section 1.1: Limits: A Numerical and Graphical Approach _ Section Objective: Find limits of functions, if they exist, using numerical or graphical methods. DEFINITON: () The of a function , as approaches , is written This means that as the values of appr

  • 3 Pages 1.2 Notes
    1.2 Notes

    School: Kennesaw

    Section 1.2: Algebraic Limits and Continuity_ Section Objectives: Develop and use the Limit Principles to calculate limits. Determine whether a function is continuous at a point. LIMIT PROPERTIES () If and we have the following: () L1 The limit of a con

  • 2 Pages 1.3 Notes
    1.3 Notes

    School: Kennesaw

    Section 1.3: Average Rates of Change _ Section Objectives: Compute an average rate of change. Find a simplified difference quotient. An The average rate of change of is the slope of a line between with respect to , as changes from ratio of the change in

  • 2 Pages 1.4 Notes
    1.4 Notes

    School: Kennesaw

    Sec 1.4: Differentiation Using Limits of Difference Quotients Section Objectives: Find derivatives and values of derivatives Find equations of tangent lines The slope of the tangent line at is This limit is also the For a function function of its define

  • 2 Pages 3.1 Notes
    3.1 Notes

    School: Kennesaw

    Section 3.1: Exponential Functions Section Objectives: Graph exponential functions. Differentiate exponential functions. DEFINITION An exponential function Where is given by is any real number, () and . The number Example 1: Graph ( ) DEFINITION: ( We c

  • 3 Pages 3.2 Notes
    3.2 Notes

    School: Kennesaw

    Section 3.2: Logarithmic Functions Section Objectives: Convert between logarithmic and exponential equations. Solve exponential equations. Solve problems involving exponential and logarithmic functions. Differentiate functions involving natural logari

  • 3 Pages 3.3 Notes
    3.3 Notes

    School: Kennesaw

    Section 3.3: Uninhibited and Limited Growth Models Section Objectives: Find functions that satisfy Convert between growth rate and doubling time. Solve application problems using exponential growth and limited growth models. RECALL Example: Differentia

  • 1 Page WS 1.5 Key pg1
    WS 1.5 Key Pg1

    School: Kennesaw

  • 1 Page WS 1.5 Key pg2
    WS 1.5 Key Pg2

    School: Kennesaw

  • 1 Page WS 1.6 Key
    WS 1.6 Key

    School: Kennesaw

  • 1 Page WS 3.1 & 3.2 Key
    WS 3.1 & 3.2 Key

    School: Kennesaw

  • 1 Page WS 3.6 Key
    WS 3.6 Key

    School: Kennesaw

  • 1 Page WS 4.1-4.3 Key
    WS 4.1-4.3 Key

    School: Kennesaw

  • 1 Page WS 4.4 Key
    WS 4.4 Key

    School: Kennesaw

  • 1 Page WS 5.1 Key
    WS 5.1 Key

    School: Kennesaw

  • 1 Page WS 1.3 & 1.4 Key
    WS 1.3 & 1.4 Key

    School: Kennesaw

  • 1 Page WS 1.1 & 1.2 Key
    WS 1.1 & 1.2 Key

    School: Kennesaw

  • 5 Pages R Notes
    R Notes

    School: Kennesaw

    Chapter R: Functions, Graphs, and Models_ Section Objectives: Defining a function and its domain/range Linear functions Quadratic functions The graph of an equation is a drawing that represents all ordered pairs that are solutions of the equation. Exam

  • 3 Pages 3.4 Notes
    3.4 Notes

    School: Kennesaw

    Section 3.4: Applications: Decay Section Objectives: Find a function that satisfies Convert between decay rate and half-life. Solve applied problems involving exponential decay. The equation , where , shows to be decreasing as a function of time, and t

  • 2 Pages 3.6 Notes
    3.6 Notes

    School: Kennesaw

    Section 3.6: An Economics Application: Elasticity of Demand Section Objectives: Find the elasticity of a demand function. Find the maximum of a total-revenue function. Characterize demand in terms of elasticity. DEFINITION The elasticity of demand () i

  • 3 Pages 4.1 Notes
    4.1 Notes

    School: Kennesaw

    Section 4.1: Antidifferentiation Section Objectives: Find an antiderivative of a function. Evaluate indefinite integrals using the basic integration formulas. Use initial conditions, or boundary conditions, to determine an antiderivative. THEOREM 1 The

  • 3 Pages 4.2 Notes
    4.2 Notes

    School: Kennesaw

    Section 4.2: Antiderivatives as Areas Section Objectives: Find the area under a graph to solve real-world problems Use rectangles to approximate the area under a graph. Example 1: A vehicle travels at 50 mi/hr for 2 hours. How far has the vehicle travel

  • 3 Pages 4.3 Notes
    4.3 Notes

    School: Kennesaw

    Section 4.3: Area and Definite Integrals Section Objectives: Find the area under a curve over a given closed interval. Evaluate a definite integral. Interpret an area below the horizontal axis. Solve applied problems involving definite integrals. DEFI

  • 3 Pages 4.4 Notes
    4.4 Notes

    School: Kennesaw

    Section 4.4: Properties of Definite Integrals Section Objectives: Use the properties of definite integrals to find the area between curves. Solve applied problems involving definite integrals. Determine the average value of a function. THEOREM 5 For Fo

  • 3 Pages 5.1 Notes
    5.1 Notes

    School: Kennesaw

    Sec 5.1: An Econ Application: Consumer & Producer Surplus Section Objectives: Given demand and supply functions, find the consumer surplus and the producer surplus at the equilibrium point. DEFINITION Suppose that consumer surplus describes the demand fu

  • 3 Pages 5.2 Notes
    5.2 Notes

    School: Kennesaw

    Section 5.2: Applications of Models Section Objectives: Perform computations involving interest compounded continuously and continuous money flow. Calculate the total consumption of a natural resource. Find the present value of an investment. Growth Fo

  • 1 Page WS 5.2 Key
    WS 5.2 Key

    School: Kennesaw

  • 5 Pages math 1106 test 1 answer key-fall 08
    Math 1106 Test 1 Answer Key-fall 08

    School: Kennesaw

    Test 1 Answers - Fall, 2008 1) x 2 6x 926 x 2 7x x 60 0 5 x 12 x x 986 0 5 Dx D5 -12 is an invalid answer x 986 5 986 981 _ 2) rate of change m 0.03 data point (x,y) 8, 1. 63 y y y m x x 1 1. 63 0. 03 x 1. 63 0. 03x y1 8 0. 24 or

  • 1 Page MATH 1106-Syllabus-Review-Statement
    MATH 1106-Syllabus-Review-Statement

    School: Kennesaw

    Course Syllabus Review Statement And Signature Form I have read the syllabus for MATH 1106, Spring Semester 2009, and have had an opportunity to ask the instructor any questions I may have about it. I understand its contents, including the course req

  • 2 Pages Chapter 3 notes
    Chapter 3 Notes

    School: Kennesaw

    Key learning issues Sections 3.1, 3.2, 3.4 Equation: Original Function First Derivative Where does it come from? Given in the problem Apply appropriate tool (power rule, chain rule, product rule, quotient rule) to original equation Apply appropriate

  • 1 Page MATH_1106_Syllabus_Review_Statement
    MATH_1106_Syllabus_Review_Statement

    School: Kennesaw

    Course Syllabus Review Statement And Signature Form I have read the syllabus for MATH 1106, Fall Semester 2008, and have had an opportunity to ask the instructor any questions I may have about it. I understand its contents, including the course requi

  • 2 Pages MATH_1106_Topic_Schedule_Fall_08
    MATH_1106_Topic_Schedule_Fall_08

    School: Kennesaw

    MATH 1106 Fall, 2008 Sections 02, 04, 06 APPROXIMATE Topic Schedule . Date Estimated section coverage Class Overhead Estimated Homework due date 8/18 8/20 8/25 8/27 9/1 9/3 9/8 9/10 9/15 1 2 3 4 5 6 7 8 9/17 9/22 9/24 9/29 10/1 10/6 9 10 11 12 1

  • 4 Pages Section 1.1LN
    Section 1.1LN

    School: Kennesaw

    Lecture Notes Section 1.1 Functions p.2 `the value of one variable depends on the value of a second one' the value of a rare coin depends upon its age the value of the rare coin is a function of its age RareCoin(x) 27.3x107 The value of Rare Coi

  • 3 Pages Section 1.2LN
    Section 1.2LN

    School: Kennesaw

    Lecture Notes Section 1.2 The graph of a function p.14, figure 1.3 - first type of calculus we study is differential calculus. One important application is finding when maximums, minimums and most rapids occur. We will explore this further beginning

  • 5 Pages Section 1.3LN
    Section 1.3LN

    School: Kennesaw

    Lecture Notes Section 1.3 Linear Functions functions whose graphs are a sraight line p.26 , example 1.3.1 Two types of cost- fixed costs and variable costs Fixed costs are costs that are incurred even if no units are produced variable costs are costs

  • 3 Pages Section 1.4LN
    Section 1.4LN

    School: Kennesaw

    Lecture Notes Load Calculator Program Section 1.4 Functional Models p.41, what are functional models mathematical representations of real situations p.54, #27 Revenue as a function of size of group R x 2400 40x Class Exercise p.55, #29 a) f(x){ 3.5x

  • 4 Pages Section 1.5LN
    Section 1.5LN

    School: Kennesaw

    Lecture Notes Section 1.5 Limits Definition: A value the output (dependent variable) of a function approaches as the input (independent variable) gets closer and closer to a stated value. A limit is not the to the same value. Example: f x same as a

  • 1 Page xref m1106 test 1 - fall 08
    Xref M1106 Test 1 - Fall 08

    School: Kennesaw

    Answer Key 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Version A 17 9 11 14 4 5 10 20 6 18 1 21 3 12 15 19 16 22 2 8 7 13 23 24 25 Version B 18 19 22 16 5 9 21 15 6 4 8 12 3 10 14 11 1 20 17 7 13 2 23 24 25

  • 13 Pages section_2.4_lecture_notes
    Section_2.4_lecture_notes

    School: Kennesaw

    Lecture Notes Section 2.4 Symmetry and Transformations Symmetry p.198 symmetry about x, y origin For symmetry imagine folding a piece of paper creased on the x axis or the y axis. p.199, Figure 1 symmetric around x axis Symmetry around x is not imp

  • 3 Pages section_2.3_lecture_notes
    Section_2.3_lecture_notes

    School: Kennesaw

    Lecture Notes Section 2.3 The Composition of Functions p.189, Composition of Functions p.197 #43 sx tx x 3 x4 x 3 x4 s x t s x x blouse size in US x blouse size in Japan t(x) blouse size in Australia s(x) blouse size in US want formula tha

  • 6 Pages math 1106 test 4 answer key-fall 08
    Math 1106 Test 4 Answer Key-fall 08

    School: Kennesaw

    MATH 1106 - test 4 key- Fall 2008 Cross Reference This cross reference will match the question numbers in the answer key to test versions 1 & 2. v.1 v.2 1 2 3 4 5 20 17 21 25 15 11 15 7 3 2 13 6 16 23 18 6 8 9 10 v.1 v.2 13 6 2 14 21 22 19 25 1 11 12

  • 1 Page MATH 1106
    MATH 1106

    School: Kennesaw

    MATH 1106 Elementary Applied Calculus Uses techniques of college algebra and elemen-tary calculus to analyze and model real world phenomena. The emphasis will be on applications using an intuitive approach to the mathematics rather than formal develo

  • 7 Pages MATH_1106_Syllabus_Fall_08
    MATH_1106_Syllabus_Fall_08

    School: Kennesaw

    MATH 1106 Elementary Applied Calculus Syllabus Spring Semester 2009 MathZone Section Code Section 04 Section 06 Section 08 MW 11:00 AM MW 12:30 PM MW 2:00 PM 12:15 PM 1:45 PM 3:15 PM BB109 BB109 BB109 F69-CD-F8F D3A-44-FCD 8F4-AF-789 ALEKS Cours

  • 7 Pages MATH1106SyllabusSpring08
    MATH1106SyllabusSpring08

    School: Kennesaw

    MATH 1106 Elementary Applied Calculus Syllabus Home.htm Spring Semester 2008 MathZone Section Code ALEKS Course Code Section 03 Section 05 Section 07 MW 11:00 AM MW 12:30 PM MW 2:00 PM 12:15 PM 1:45 PM 3:15 PM BB109 BB109 BB109 69E-3F-9DD

  • 4 Pages optprobs
    Optprobs

    School: Kennesaw

    Optimization Problems 1. A farmer with 2400 ft of fencing wants to construct a rectangular pen that will border a straight river. He needs no fence along the river. What are the dimensions of the pen of largest of area that the farmer can build? 2. A

  • 90 Pages ch02
    Ch02

    School: Kennesaw

    CHAPTER 2 The acceleration of a moving object is found by differentiating its velocity. DIFFERENTIATION: BASIC CONCEPTS 1 2 3 4 5 6 The Derivative Techniques of Differentiation Product and Quotient Rules; Higher-Order Derivatives The Chain Rule Mar

  • 3 Pages section_2.1_lecture_notes
    Section_2.1_lecture_notes

    School: Kennesaw

    Lecture Notes Section 2.1 Increasing, Decreasing and Piecewise Functions p.166, Increasing, Decreasing and Constant Functions mechanical answer increasing if it rises from left to right decreasing if it drops from left to right constant if it neit

  • 4 Pages section_2.2_lecture_notes
    Section_2.2_lecture_notes

    School: Kennesaw

    Lecture Notes Section 2.2 The Alegbra of Functions P.182 Combination of functions - Sums, Differences, Products and Quotients of Functions We can create new functions through the four operations listed. The Algebra is simple. The issue is determining

  • 2 Pages Section 1.6LN
    Section 1.6LN

    School: Kennesaw

    Lecture Notes Section 1.6 One-sided Limits and Continuity p.73, figure 1.50 common sense definition of continuity-can I draw the graph of the function without lifting my pencil off the paper? A is continuous B is not continuous at x b When function

  • 3 Pages Section 2.1LN
    Section 2.1LN

    School: Kennesaw

    Lecture Notes Section 2.1 The Derivative p.98 Calculus is the mathematics of change Developed by Newton and Leibniz in 15th-16th century p.98 rates of change and slope figure 2.1 contrast between linear rate of change (slope) and non-linear rate of c

  • 3 Pages Section 2.2LN
    Section 2.2LN

    School: Kennesaw

    Lecture Notes Section 2.2 Techniques of Differentiation p.113 The constant rule The graph of a constant is a horizontal line. Regardless of value of x, y constant The slope of a horizontal line is 0 The derivative of a constant is 0 p.113 The power r

  • 2 Pages Section 5.3LN
    Section 5.3LN

    School: Kennesaw

    Lecture Notes Section 5.3 starts on p.386 Definite Integral definition The area between the graph of a function and the horizontal axis within a specified interval. p.388, rectangle method of approximating area divide the area desired into uniform wi

  • 5 Pages Section 5.4LN
    Section 5.4LN

    School: Kennesaw

    Lecture Notes Section 5.4 Area Between Curves and Average Value p.404 Area between curves picture p.404 Steps 1) If interval is given in the problem go to next step. Otherwise determine the interval by setting f(x) g(x). Solve for x which gives the

  • 4 Pages Section 5.5LN
    Section 5.5LN

    School: Kennesaw

    Lecture Notes Section 5.5 Additional Applications to Business and Economics Useful life of a machine,p.421 The useful life of a machine is until it's cost exceeds it's revenue. Where does C t p.421, ex 5.5.1 R t R t 5000 20t 2 20t 2 C t a)5000

  • 5 Pages m1106 test 1 answer key- spring-08
    M1106 Test 1 Answer Key- Spring-08

    School: Kennesaw

    MATH 1106 Test 1 Answers Spring 2008 Questions are ordered based on test version 1. To find the matching question for test 2 use the following cross reference table: v.1 v.2 1 2 3 4 5 22 13 * 20 * 6 11 v.1 v.2 6 7 8 9 10 8 18 3 10 * 12 v.1 v.2 11

  • 6 Pages m1106 test 1 answer key- spring-09
    M1106 Test 1 Answer Key- Spring-09

    School: Kennesaw

    Test 1 Answers - Spring, 2009 Multiple choice answers # 1 2 3 4 5 6 7 8 9 10 11 V1 B B B D C C D D B B V2 C D A D B B B C A C # 12 13 14 15 16 17 18 19 20 21 22 V1 C B B B C D A A B B A V2 D D C A A D A C C A B Cross Reference Answer Key versus Vers

  • 5 Pages m1106 test 2 answer key spring-08
    M1106 Test 2 Answer Key Spring-08

    School: Kennesaw

    MATH 1106 Test 2 Answer Key Spring, 2008 To find the matching question for test 1 or test 2 use the following cross reference table: key v.1 v.2 1 2 3 4 5 21 22 23 24 25 7 9 18 16 8 5 12 25 23 24 12 8 4 18 11 7 20 24 25 23 key v.1 v.2 6 7 8 9 10 15

  • 5 Pages m1106 test 2 answer key spring-09
    M1106 Test 2 Answer Key Spring-09

    School: Kennesaw

    Math 1106 Test 2 Spring 2009 Answer Key Cross Reference This cross reference will match the question numbers in the answer key to test versions 1 & 2. v.1 v.2 1 2 3 4 5 11 9 18 16 19 13 15 5 7 9 4 20 24 25 23 6 7 8 9 v.1 13 10 14 x5 v.2 10 22 21 x

  • 5 Pages m1106 test 3 answer key spring-08
    M1106 Test 3 Answer Key Spring-08

    School: Kennesaw

    Math 1106 Test 03 Spring 08 Answer Key To find the matching question for test 1 or test 2 use the following cross reference table: key v.1 v.2 1 2 3 4 5 21 22 23 24 25 5 22 4 17 3 16 19 25 23 24 3 18 8 10 22 20 17 23 24 25 key v.1 v.2 6 7 8 9 10 15

  • 2 Pages Section 5.1LN
    Section 5.1LN

    School: Kennesaw

    Lecture Notes Section 5.1 The Indefinite Integral Integration is the opposite of differentiation. can use rate of change in population to predict future population rate of change in profit to predict future profit Instead of derivative we have anti-d

  • 1 Page Section 4.4LN
    Section 4.4LN

    School: Kennesaw

    Lecture Notes Section 4.4 Additional Exponential Models p.343 #31 a) L(t) ln t1 t1 t1 1 t1 L t L t 0 ln t1 1 t1 2 1 ln t1 t1 2 1 ln t1 t1 2 01 ln t 1 ln t 1 1 e1 t 1 te 1 critical point end points t0 t5 L(0) L(5) L(e) ln 01 01 ln 51 51

  • 2 Pages Section 4.3LN
    Section 4.3LN

    School: Kennesaw

    Lecture Notes Section 4.3 Differentiation of Logarithmic and Exponential Functions * NOT COVERED FALL 2008 * p.319 f(x)ln x p.319 ex. 4.3.1 f(x)x ln (x) 1 x f'(x) 1 x product rule f'(x)(1)ln (x)( (x)ln(x) 1 Class Exercise p.330 #15 f x x 2 ln x

  • 4 Pages Section 2.3LN
    Section 2.3LN

    School: Kennesaw

    Lecture Notes Section 2.3 Product and Quotient Rules: Higher Order Derivatives. p.125 Product Rule - used when two expressions are multiplied together. Derivative of first factor Second factor Derivative of second factor First factor Or. Cross

  • 4 Pages Section 2.4LN
    Section 2.4LN

    School: Kennesaw

    Lecture Notes Section 2.4 The Chain Rule There are two versions of the chain rule. Both are useful depending upon the situation. Chain Rule #1 p.143 Author calls it "The General Power Rule" Used to find the derivative of algebraic expressions to a po

  • 2 Pages Section 2.5LN
    Section 2.5LN

    School: Kennesaw

    Lecture Notes Section 2.5 Marginal Analysis and Approximations Using Increments p.152 Marginal Analysis use the derivative to APPROXIMATE change by one unit derivative of profit is marginal profit derivative of cost is marginal cost derivative of rev

  • 2 Pages Section 3.1LN
    Section 3.1LN

    School: Kennesaw

    Lecture Notes Section 3.1 Increasing and Decreasing Functions; Relative Extrema p.188 bottom - increasing function rising from left to right; as x value increases y value increases decreasing function falling from left to right as x value increases,

  • 4 Pages Section 3.2LN
    Section 3.2LN

    School: Kennesaw

    Lecture Notes Section 3.2 Concavity and Points of Inflection p.204 graph on bottom of page Point of diminishing return is where maximum efficiency (maximum rate of change) occurs. This is called the inflection point or point of inflection. Derivative

  • 4 Pages Section 3.4LN
    Section 3.4LN

    School: Kennesaw

    Lecture Notes Section 3.4 Optimization p.236 Graph at top of page Absolute extrema occurring within a specified interval bottom of p.236 absolute extrema versus relative extrema Closed intervals End points are included [a,b] is interval notation. a x

  • 4 Pages Section 4.1LN
    Section 4.1LN

    School: Kennesaw

    Lecture Notes Section 4.1 Exponential Functions p.289 bottom of page standard format for exponential function f(x)b x called an exponential function because the variable is in the exponent x is the exponent a short hand notation for base times itself

  • 2 Pages Section 4.2LN
    Section 4.2LN

    School: Kennesaw

    Lecture Notes Section 4.2 Logarithmic Functions Logarithmic functions reverse the process of exponentation. p.303 logarithmic function f(x) log b x or y log b if and only if b y What is a log? 100) log 10 100 2 the base to what power equals 100 x fo

  • 5 Pages m1106 test 4 answer key spring-08
    M1106 Test 4 Answer Key Spring-08

    School: Kennesaw

    Math 1106 - Spring 08 Test 4 answer key Question Number Cross Reference Answers KEY V 1 V2 1 2 3 4 5 6 7 8 9 10 11 12 13 16 9 21 14 13 17 1 20 10 11 4 15 7 10 5 9 18 12 19 14 6 22 2 7 1 3 V1 V2 1 2 3 4 5 6 7 8 9 D C A A D A D C C B B D B A A C A D B

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