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### finalsp07sampleprobs

Course: KFS 2007, Fall 2009
School: CSU Northridge
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Word Count: 1069

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Questions Sample for the Math 103 Final Exam May 2007 Calculators are not permitted on the actual nal exam. The actual nal exam will have fewer question; these problems are intended as a study guide. 1. Draw an accurate graph of the function f (x) = 2x + 5. Show the intercepts and write their coordinates on the graph. 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 1 2 3 4 5 6 Find the slope-intercept form for...

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Questions Sample for the Math 103 Final Exam May 2007 Calculators are not permitted on the actual nal exam. The actual nal exam will have fewer question; these problems are intended as a study guide. 1. Draw an accurate graph of the function f (x) = 2x + 5. Show the intercepts and write their coordinates on the graph. 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 1 2 3 4 5 6 Find the slope-intercept form for the equation of the line whose graph is shown below: 4 3 2 1 -4 -3 -2 -1 -1 1 2 3 4 -2 -3 -4 1 2. Find the derivatives of the following functions. (a) f (x) = 2x3 3x + 7 (b) g(x) = ln(x) x (Simplify this derivative.) 2x2 x + 3 (d) k(x) = e2x+7 (c) h(x) = (e) r(x) = x ln(x) (f) s(x) = ex (g) t(x) = (2x4 x3 + 3x2 7)(x3 + x2 2) 3. Find the equation for the line tangent to the curve f (x) at the point (1, 9): f (x) = 3x2 x + 7 4. Find the absolute maximum and minimum values for the function f (x) = x3 6x2 + 9x + 1, on the interval [0, 2]. 5. Suppose we have an \$6000 to invest. (a) What amount will our account have after 10 years if is invested at an annual rate of 3% compounded semi-annually. (b) How long will it take for our account to grow to \$12,000 if it is invested at an annual rate of 3% compounded continuously. 2 6. Consider the following function. x3 , x + 3, f (x) = 7, if x 2 if 2 < x < 4 if x 4 (a) Where is this function discontinuous? Why? (b) Where is this function dierentiable? Why? 7. A company manufactures and sells x units per week. The weekly price demand and cost functions are: x p(x) = 4 50 C(x) = 25 + x. (a) Find the production level that will maximize prot and the price the company should charge for each unit. (b) Explain in words why the value x for which prot is maximized is the same as the x value for which the slope of the tangent line to the revenue function is the same as that of the cost function. (c) If the xed production costs increase from 25 to 30, will your answer to (a) change? How? Why? (Note: You do not have to compute here.) 8. Continuing with a company manufactures and sells x units per week. The weekly price demand and cost functions are: p(x) = 4 x 50 C(x) = 25 + x. Graph the revenue and cost functions. You do not have to nd the break-even points. (But it is not a bad idea to do this for practice.) (a) Label the axes and mark the scale (tick marks) on the axes; 3 (b) Label y = R(x), its x-intercepts, its maximum point with coordinates; (c) Label y = C(x), its y-intercept and one other point on y = C(x). (d) Shade the areas which correspond to the company making a prot make a bold line to represent the maximum prot graphically. 100 75 9. Continuing with a company manufactures and sells x units per week with weekly pricex demand equation: p = 4 50 (a) Use the price-demand equation to solve for x in terms of p to get a function f (p) which gives the demand as a function of the price p. (b) Compute the elasticity of demand function for this price-demand function. (c) At p = \$3: a price increase of 10% will create a demand decrease of what percent? (d) Is the revenue function or increasing decreasing at a price of \$3 per unit? 4 10. A company manufactures and sells x units per week. The price demand equation is of the form p = ax + b. When the price is \$7 the demand is 2 units and when the price is \$9, the demand is 1 unit. Find a and b. Suppose that the supply x and price p are related by the equation p = 2x + 3. (a) Find the equilibrium price and quantity. (b) Find the augmented matrix that represents this system of equations you solved in (a). Remark: Other questions here could be: Find the supply function instead of nd the demand function. Solve the system of equations using matrices. Graph the lines. Look also at problems 61-66 in 4.4 homework problems in text (I would use easier numbers). 11. Alpha Metal Works is considering producing and selling aardvark cages. The research department estimates that the xed costs to retool and the manufacture the new cages will be \$1,200 and the variable costs will be \$10 per cage. (a) Write an algebraic expression for the cost function to produce x cages: C(x) = (b) The price-demand equation for the aardvark cages is p + (0.6)x = 120. Price is given in dollars, and x is the demand at price p. Write an algebraic expression for revenue as a function of demand. R(x) = 12. Beta Borax Inc. plans to introduce a new shower cleaner. The cost (in dollars) to produce x tons of cleaner is C(x) = 3000 + 25x. The price-demand equation is p = 100 (0.5)x. 5 (a) Write an expression for revenue as a function of demand: R(x) = (b) Compute the marginal cost and marginal revenue functions: Marginal cost: Marginal revenue: (c) Use the marginal revenue function to approximate the revenue for selling the 11th ton of cleaner. 13. Gamma Gum Works makes and sells chewing gum. The price-demand equation is x = 100 2p, where x is the demand (in pounds) for chewing gum at a price of p (in ...

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CSU Northridge - KFS - 103
NAME: Math 103 Fall 2006: Final version 3. General InstructionsClass time:1. You are allowed your cheatsheat (one page, front and back). 2. NO Calculators. 3. Please show all your work, unless explicitly instructed not to do so. 4. Please ask if
CSU Northridge - KFS - 4816
NAME: Math 103 Fall 2006: Final version 3. General InstructionsClass time:1. You are allowed your cheatsheat (one page, front and back). 2. NO Calculators. 3. Please show all your work, unless explicitly instructed not to do so. 4. Please ask if
CSU Northridge - KFS - 103
NAME: Math 103 Fall 2006: Final version 1. General InstructionsClass time:1. You are allowed your cheatsheat (one page, front and back). 2. NO Calculators. 3. Please show all your work, unless explicitly instructed not to do so. 4. Please ask if
CSU Northridge - KFS - 4816
NAME: Math 103 Fall 2006: Final version 1. General InstructionsClass time:1. You are allowed your cheatsheat (one page, front and back). 2. NO Calculators. 3. Please show all your work, unless explicitly instructed not to do so. 4. Please ask if
CSU Northridge - KFS - 103
NAME: Math 103 Fall 2006: Practice Final. General InstructionsClass time:1. You are allowed your cheatsheat (one page, front and back). 2. NO Calculators. 3. Please show all your work, unless explicitly instructed not to do so. 4. Please ask if y
CSU Northridge - KFS - 4816
NAME: Math 103 Fall 2006: Practice Final. General InstructionsClass time:1. You are allowed your cheatsheat (one page, front and back). 2. NO Calculators. 3. Please show all your work, unless explicitly instructed not to do so. 4. Please ask if y
CSU Northridge - KFS - 103
NAME: Math 103 Fall 2006: Practice Final. General InstructionsClass time:1. You are allowed your cheatsheat (one page, front and back). 2. NO Calculators. 3. Please show all your work, unless explicitly instructed not to do so. 4. Please ask if y
CSU Northridge - KFS - 4816
NAME: Math 103 Fall 2006: Practice Final. General InstructionsClass time:1. You are allowed your cheatsheat (one page, front and back). 2. NO Calculators. 3. Please show all your work, unless explicitly instructed not to do so. 4. Please ask if y
CSU Northridge - KFS - 103
NAME: INSTRUCTORs NAME: Math 103 Spring 2007:General Instructions 1. NO Calculators. 2. Please show all your work, unless explicitly instructed not to do so. 3. Please ask if you are not sure of anything on the exam. 4. You have 120 minutes.Quest
CSU Northridge - KFS - 2007
NAME: INSTRUCTORs NAME: Math 103 Spring 2007:General Instructions 1. NO Calculators. 2. Please show all your work, unless explicitly instructed not to do so. 3. Please ask if you are not sure of anything on the exam. 4. You have 120 minutes.Quest
CSU Northridge - KFS - 103
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CSU Northridge - KFS - 2007
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CSU Northridge - KFS - 103
NAME: Math 103 Fall 2006: Final version 2. General InstructionsClass time:1. You are allowed your cheatsheat (one page, front and back). 2. NO Calculators. 3. Please show all your work, unless explicitly instructed not to do so. 4. Please ask if
CSU Northridge - KFS - 4816
NAME: Math 103 Fall 2006: Final version 2. General InstructionsClass time:1. You are allowed your cheatsheat (one page, front and back). 2. NO Calculators. 3. Please show all your work, unless explicitly instructed not to do so. 4. Please ask if
CSU Northridge - KFS - 103
NAME: INSTRUCTORs NAME: Math 103 Spring 2007:General Instructions 1. NO Calculators. 2. Please show all your work, unless explicitly instructed not to do so. 3. Please ask if you are not sure of anything on the exam. 4. You have 120 minutes.Quest
CSU Northridge - KFS - 2007
NAME: INSTRUCTORs NAME: Math 103 Spring 2007:General Instructions 1. NO Calculators. 2. Please show all your work, unless explicitly instructed not to do so. 3. Please ask if you are not sure of anything on the exam. 4. You have 120 minutes.Quest
CSU Northridge - KFS - 103
NAME: INSTRUCTORs NAME: Makeup Math 103 Spring 2007:General Instructions 1. NO Calculators. 2. Please show all your work, unless explicitly instructed not to do so. 3. Please ask if you are not sure of anything on the exam. 4. You have 120 minutes.
CSU Northridge - KFS - 2007
NAME: INSTRUCTORs NAME: Makeup Math 103 Spring 2007:General Instructions 1. NO Calculators. 2. Please show all your work, unless explicitly instructed not to do so. 3. Please ask if you are not sure of anything on the exam. 4. You have 120 minutes.
CSU Northridge - KFS - 103
Examples Review for Exam ILinear equations and lines Functions and units of measurement Shift, stretch, squish, flip Piecewise Linear functionsFind the equation of the line through (1,5) with slope 4/7.Find the equation of the line through (1,5)
CSU Northridge - KFS - 4816
Examples Review for Exam ILinear equations and lines Functions and units of measurement Shift, stretch, squish, flip Piecewise Linear functionsFind the equation of the line through (1,5) with slope 4/7.Find the equation of the line through (1,5)
CSU Northridge - KFS - 320
Project Notes for Math 320: Fundamentals of Mathematics Operations, closure, and groups.August 31, 20051Introduction to OperationsDenition 1.1. 1. Given a set X an operation, call it , on X is a rule that takes any two elements x, y X and co
CSU Northridge - KFS - 4816
Project Notes for Math 320: Fundamentals of Mathematics Operations, closure, and groups.August 31, 20051Introduction to OperationsDenition 1.1. 1. Given a set X an operation, call it , on X is a rule that takes any two elements x, y X and co
CSU Northridge - KFS - 320
Course Notes for Math 320: Fundamentals of Mathematics Chapter 3: Induction.February 21, 20061Proof by InductionDenition 1.1. A subset S of the natural numbers is said to be inductive if n S we have n + 1 S. Example 1.2. Which sets are induc
CSU Northridge - KFS - 4816
Course Notes for Math 320: Fundamentals of Mathematics Chapter 3: Induction.February 21, 20061Proof by InductionDenition 1.1. A subset S of the natural numbers is said to be inductive if n S we have n + 1 S. Example 1.2. Which sets are induc
CSU Northridge - KFS - 320
Course Notes for Math 320: Fundamentals of Mathematics Chapter 1: Generalities on proofs.September 2, 20051Propositions, TruthDenition 1.1 A proposition is a sentence that is either true or false. Example 1.2 Which one is a proposition? 1. Thi
CSU Northridge - KFS - 4816
Course Notes for Math 320: Fundamentals of Mathematics Chapter 1: Generalities on proofs.September 2, 20051Propositions, TruthDenition 1.1 A proposition is a sentence that is either true or false. Example 1.2 Which one is a proposition? 1. Thi
CSU Northridge - KFS - 320
Course Notes for Math 320: Fundamentals of Mathematics Chapter 5: Functions.November 2, 20051Introduction to FunctionsDenition 1.1. 1. A function is a (non-empty) relation f such that if a is in the domain of f then there is ONE AND ONLY ONE o
CSU Northridge - KFS - 4816
Course Notes for Math 320: Fundamentals of Mathematics Chapter 5: Functions.November 2, 20051Introduction to FunctionsDenition 1.1. 1. A function is a (non-empty) relation f such that if a is in the domain of f then there is ONE AND ONLY ONE o
CSU Northridge - KFS - 320
Project Notes for Math 320: Fundamentals of Mathematics More on Equivalence Relations.W. Watkins September 5, 200511.1Equivalence Relationsquadratic polynomialsLet Q be the set of all real quadratic polynomials. That is Q = {a0 + ax + a2 x2
CSU Northridge - KFS - 4816
Project Notes for Math 320: Fundamentals of Mathematics More on Equivalence Relations.W. Watkins September 5, 200511.1Equivalence Relationsquadratic polynomialsLet Q be the set of all real quadratic polynomials. That is Q = {a0 + ax + a2 x2
CSU Northridge - KFS - 320
NAME: Homework 3 supplement: Fundamentals of Mathematics (Math 320) StevensonLet P2 be the set of all polynomials with coecients in R and in variable x of degree less than or equal to 2. That is, P2 = f (x) = a0 + a1 x + a2 x2 | a0 , a1 , a2 R . F
CSU Northridge - KFS - 4816
NAME: Homework 3 supplement: Fundamentals of Mathematics (Math 320) StevensonLet P2 be the set of all polynomials with coecients in R and in variable x of degree less than or equal to 2. That is, P2 = f (x) = a0 + a1 x + a2 x2 | a0 , a1 , a2 R . F
CSU Northridge - KFS - 320
Project Notes for Math 320: Fundamentals of Mathematics Countability.August 24, 20051Introduction to Finite, countable, and uncountable setsDenition 1.1. Consider the following relation on sets: ST a bijective function f : S T.Remark 1.2
CSU Northridge - KFS - 4816
Project Notes for Math 320: Fundamentals of Mathematics Countability.August 24, 20051Introduction to Finite, countable, and uncountable setsDenition 1.1. Consider the following relation on sets: ST a bijective function f : S T.Remark 1.2
CSU Northridge - KFS - 320
Project Notes for Math 320: Fundamentals of Mathematics Postage Problem, Part 1.September 19, 20051The problemA few days ago, I had to send a letter by Priority Mail, which costs \$3.85. A regular rstclass letter costs 37 cents for the rst oun
CSU Northridge - KFS - 4816
Project Notes for Math 320: Fundamentals of Mathematics Postage Problem, Part 1.September 19, 20051The problemA few days ago, I had to send a letter by Priority Mail, which costs \$3.85. A regular rstclass letter costs 37 cents for the rst oun
CSU Northridge - KFS - 320
Exercise on Equivalence relations and invariantsK.F. Stevenson and W. Watkins April 22, 200511.1Equivalence Relationsquadratic polynomialsLet Q be the set of all real quadratic polynomials. That is Q = {a0 + ax + a2 x2 | ai R}. Dene a relat
CSU Northridge - KFS - 4816
Exercise on Equivalence relations and invariantsK.F. Stevenson and W. Watkins April 22, 200511.1Equivalence Relationsquadratic polynomialsLet Q be the set of all real quadratic polynomials. That is Q = {a0 + ax + a2 x2 | ai R}. Dene a relat
CSU Northridge - KFS - 103
NAME: Math 103 Fall 2006: Practice Final. General InstructionsClass time:1. You are allowed your cheatsheat (one page, front and back). 2. NO Calculators. 3. Please show all your work, unless explicitly instructed not to do so. 4. Please ask if y
CSU Northridge - KFS - 4816
NAME: Math 103 Fall 2006: Practice Final. General InstructionsClass time:1. You are allowed your cheatsheat (one page, front and back). 2. NO Calculators. 3. Please show all your work, unless explicitly instructed not to do so. 4. Please ask if y
CSU Northridge - KFS - 103
NAME: Math 103L: Quadratics and general polynomials (Section 2.3) These problems are a sample of the kinds of problems that may appear on the nal exam. Some answers are included to indicate what is expected. Problems that require a summary statement
CSU Northridge - KFS - 4816
NAME: Math 103L: Quadratics and general polynomials (Section 2.3) These problems are a sample of the kinds of problems that may appear on the nal exam. Some answers are included to indicate what is expected. Problems that require a summary statement
CSU Northridge - KFS - 103
Math 103 Practice Problems for the FinalMay 21, 2008These problems are a sample of the kinds of problems that may appear on the nal exam. Some answers are included to indicate what is expected. Problems that require a summary statement are marked
CSU Northridge - KFS - 4816
Math 103 Practice Problems for the FinalMay 21, 2008These problems are a sample of the kinds of problems that may appear on the nal exam. Some answers are included to indicate what is expected. Problems that require a summary statement are marked
CSU Northridge - KFS - 103
Tutoring Center SH 274 Comp. Lab see bottom for hours WeekMon.-Thurs 10-5:30;Friday 10-3; Sat. 11-2SyllabusInstructor information Click HERE for practice problems for the finalWebwork:webwork.csun.eduTopicHr 1Hr 2Hr 3Lab8/25/0
CSU Northridge - KFS - 4816
Tutoring Center SH 274 Comp. Lab see bottom for hours WeekMon.-Thurs 10-5:30;Friday 10-3; Sat. 11-2SyllabusInstructor information Click HERE for practice problems for the finalWebwork:webwork.csun.eduTopicHr 1Hr 2Hr 3Lab8/25/0
CSU Northridge - KFS - 103
Math 103 Sample FinalOctober 1, 2007These problems are a sample of the kinds of problems that may appear on the nal exam. Some answers are included to indicate what is expected. Problems that require a summary statement are marked with Sum . The
CSU Northridge - KFS - 4816
Math 103 Sample FinalOctober 1, 2007These problems are a sample of the kinds of problems that may appear on the nal exam. Some answers are included to indicate what is expected. Problems that require a summary statement are marked with Sum . The
CSU Northridge - KFS - 103
NAME: Math 103L: Rational functions (Section 2.3 end).1. Relative to the graph of 1 , x+1 the graphs of the following equations have been changed in what way? y= Answer 5 1. y = x+1 1 2. y = (x + 5) + 1 1 3. y = 5 x+1 A B C shifted 5 units right s
CSU Northridge - KFS - 4816
NAME: Math 103L: Rational functions (Section 2.3 end).1. Relative to the graph of 1 , x+1 the graphs of the following equations have been changed in what way? y= Answer 5 1. y = x+1 1 2. y = (x + 5) + 1 1 3. y = 5 x+1 A B C shifted 5 units right s
CSU Northridge - KFS - 103
WARM UP EXERCSEA company makes and sells inline skates. The price-demand function is p (x) = 190 0.013(x 10)2. Describe how the graph of function p can be obtained from one of the library functions. Sketch the function.1 1-3 Linear Functions &amp;
CSU Northridge - KFS - 4816
WARM UP EXERCSEA company makes and sells inline skates. The price-demand function is p (x) = 190 0.013(x 10)2. Describe how the graph of function p can be obtained from one of the library functions. Sketch the function.1 1-3 Linear Functions &amp;
CSU Northridge - KFS - 103
WARM UP EXERCSEYou deposit \$100 in the bank at 10% annual rate with the intention of leaving it there for one year. You expect to have \$_ at the end of the year. After four months you have a bad day and you withdraw the money. They give you \$__. But
CSU Northridge - KFS - 4816
WARM UP EXERCSEYou deposit \$100 in the bank at 10% annual rate with the intention of leaving it there for one year. You expect to have \$_ at the end of the year. After four months you have a bad day and you withdraw the money. They give you \$__. But
CSU Northridge - KFS - 4816
Local Galois theory in dimension two David Harbater and Katherine F. Stevenson Abstract. This paper proves a generalization of Shafarevichs Conjecture, for elds of Laurent series in two variables over an arbitrary eld. This result says that the absol
CSU Northridge - SOM - 2035
Stanford University Graduate School of BusinessNovember 1998Littlefield Technologies: OverviewIntroductionLittlefield Technologies is a job shop which assembles Digital Satellite System receivers. These receivers are assembled from kits of elec
CSU Northridge - AA - 306
Stanford University Graduate School of BusinessNovember 1998Littlefield Technologies: OverviewIntroductionLittlefield Technologies is a job shop which assembles Digital Satellite System receivers. These receivers are assembled from kits of elec
CSU Northridge - SOM - 2035
Stanford University Graduate School of Businessrev. August 2004Managing Customer Responsiveness at Littlefield TechnologiesBackgroundLittlefield Technologies (LT) has developed another DSS product. The new product is manufactured using the same
CSU Northridge - AA - 2035
Stanford University Graduate School of Businessrev. August 2004Managing Customer Responsiveness at Littlefield TechnologiesBackgroundLittlefield Technologies (LT) has developed another DSS product. The new product is manufactured using the same
CSU Northridge - AA - 306
Stanford University Graduate School of Businessrev. August 2004Managing Customer Responsiveness at Littlefield TechnologiesBackgroundLittlefield Technologies (LT) has developed another DSS product. The new product is manufactured using the same
CSU Northridge - AA - 2035
Stanford University Graduate School of Businessrev. Jan. 1999Capacity Management at Littlefield TechnologiesBackgroundIn early January, Littlefield Technologies (LT) opened its first and only factory to produce its newly developed Digital Satel