Solutions for Precalculus: Mathematics for Calculus (Standalone Book)
Problem 1E:
Give an example of each of the following: (a) A natural number (b) An integer that is not a natural...Problem 2E:
Complete each statement and name the property of real numbers you have used. (a) ab = __________;...Problem 3E:
Express the set of real numbers between but not including 2 and 7 as follows. (a) In set-builder...Problem 4E:
The symbol | x | stands for the __________of the number x. If x is not 0, then the sign of | x | is...Problem 5E:
The distance between a and b on the real line is d(a, b) = __________. So the distance between 5 and...Problem 6E:
Yes or No? If No, give a reason. Assume that a and b are nonzero real numbers. 6. (a) Is the sum of...Problem 7E:
Yes or No? If No, give a reason. Assume that a and b are nonzero real numbers. 7. (a) Is a b equal...Problem 8E:
Yes or No? If No, give a reason. Assume that a and b are nonzero real numbers. 8. (a) Is the...Problem 9E:
Real Numbers List the elements of the given set that are (a) natural numbers (b) integers (c)...Problem 10E:
Real Numbers List the elements of the given set that are (a) natural numbers (b) integers (c)...Problem 11E:
Properties of Real Numbers State the property of real numbers being used. 11. 3 + 7 = 7 + 3Problem 13E:
Properties of Real Numbers State the property of real numbers being used. 13. (x + 2y) + 3z = x +...Problem 14E:
Properties of Real Numbers State the property of real numbers being used. 14. 2(A + B) = 2A + 2BProblem 15E:
Properties of Real Numbers State the property of real numbers being used. 15. (5x + 1)3 = 15x + 3Problem 16E:
Properties of Real Numbers State the property of real numbers being used. 16. (x + a)(x + b) = (x +...Problem 17E:
Properties of Real Numbers State the property of real numbers being used. 17. 2x(3 + y) = (3 + y)2xProblem 18E:
Properties of Real Numbers State the property of real numbers being used. 18. 7(a + b + c) = 7(a +...Problem 19E:
Properties of Real Numbers Rewrite the expression using the given property of real numbers. 19....Problem 21E:
Properties of Real Numbers Rewrite the expression using the given property of real numbers. 21....Problem 22E:
Properties of Real Numbers Rewrite the expression using the given property of real numbers. 22....Problem 25E:
Properties of Real Numbers Use properties of real numbers to write the expression without...Problem 26E:
Properties of Real Numbers Use properties of real numbers to write the expression without...Problem 27E:
Properties of Real Numbers Use properties of real numbers to write the expression without...Problem 32E:
Arithmetic Operations Perform the indicated operations. 32. (a) 223322 (b) 25+12110+315Problem 33E:
Inequalities Place the correct symbol (, , or =) in the space. 33. (a) 372 (b) 372 (c) 3.572Problem 36E:
Inequalities State whether each inequality is true or false. 36. (a) 31.7325 (b) 1.73253Problem 39E:
(a) x is positive. (b) t is less than 4. (c) a is greater than or equal to . (d) x is less than 13...Problem 44E:
Sets Find the indicated set if A=1,2,3,4,5,6,7B=2,4,6,8C=7,8,9,10 44. (a) A B C (b) A B CProblem 47E:
Intervals Express the interval in terms of inequalities, and then graph the interval. 47. (3, 0)Problem 48E:
Intervals Express the interval in terms of inequalities, and then graph the interval. 48. (2, 8]Problem 49E:
Intervals Express the interval in terms of inequalities, and then graph the interval. 49. [2, 8)Problem 51E:
Intervals Express the interval in terms of inequalities, and then graph the interval. 51. [2, )Problem 52E:
Intervals Express the interval in terms of inequalities, and then graph the interval. 52. (, 1)Problem 53E:
Intervals Express the inequality in interval notation, and then graph the corresponding interval....Problem 55E:
Intervals Express the inequality in interval notation, and then graph the corresponding interval....Problem 61E:
Intervals Graph the set. 61. (2, 0) (1, 1)Problem 62E:
Intervals Graph the set. 62. (2, 0) (1, 1)Problem 63E:
Intervals Graph the set. 63. [4, 6] [0, 8)Problem 65E:
Intervals Graph the set. 65. (, 4) (4, )Problem 66E:
Intervals Graph the set. 66. (, 6] (2, 10)Problem 75E:
Distance Find the distance between the given numbers. 75. (a) 2 and 17 (b) 3 and 21 (c) 118and310Problem 76E:
(a) 715and121 (b) 38 and 57 (c) 2.6 and 1.8Problem 77E:
Repeating Decimal Express each repeating decimal as a fraction. (See the margin note on page 3.) 77....Problem 81E:
Simplifying Absolute Value Express the quantity without using absolute value. 81. |a b|, where a bProblem 83E:
Signs of Numbers Let a, b, and c be real numbers such that a 0, b 0, and c 0. Find the sign of...Problem 85E:
Area of a Garden Marys backyard vegetable garden measures 20 ft by 30 ft, so its area is 20 30 =...Problem 86E:
Temperature Variation The bar graph shows the daily high temperatures for Omak, Washington, and...Problem 87E:
Mailing a Package The post office will accept only packages for which the length plus the girth...Problem 88E:
DISCUSS: Sums and Products of Rational and Irrational Numbers Explain why the sum, the difference,...Problem 89E:
DISCOVER PROVE: Combining Rational and Irrational Numbers Is 12+2 rational or irrational? Is...Problem 90E:
DISCOVER: Limiting Behavior of Reciprocals Complete the tables. What happens to the size of the...Problem 91E:
DISCOVER: Locating Irrational Numbers on the Real Line Using the figures below, explain how to...Problem 92E:
PROVE: Maximum and Minimum Formulas Let max(a, b) denote the maximum and min(a, b) denote the...Problem 93E:
WRITE: Real Numbers in the Real World Write a paragraph describing different real-world situations...Browse All Chapters of This Textbook
Chapter 1 - FundamentalsChapter 1.1 - Real NumbersChapter 1.2 - Exponents And RadicalsChapter 1.3 - Algebraic ExpressionsChapter 1.4 - Rational ExpressionsChapter 1.5 - EquationsChapter 1.6 - Complex NumbersChapter 1.7 - Modeling With EquationsChapter 1.8 - InequalitiesChapter 1.9 - The Coordinate Plane; Graphs Of Equations; Circles
Chapter 1.10 - LinesChapter 1.11 - Solving Equations And Inequalities GraphicallyChapter 1.12 - Modeling VariationChapter 2 - FunctionsChapter 2.1 - FunctionsChapter 2.2 - Graphs Of FunctionsChapter 2.3 - Getting Information From The Graph Of A FunctionChapter 2.4 - Average Rate Of Change Of A FunctionChapter 2.5 - Linear Functions And ModelsChapter 2.6 - Transformations Of FunctionsChapter 2.7 - Combining FunctionsChapter 2.8 - One-to-one Functions And Their InversesChapter 3 - Polynomial And Rational FunctionsChapter 3.1 - Quadratic Functions And ModelsChapter 3.2 - Polynomial Functions And Their GraphsChapter 3.3 - Dividing PolynomialsChapter 3.4 - Real Zeros Of PolynomialsChapter 3.5 - Complex Zeros And The Fundamental Theorem Of AlgebraChapter 3.6 - Rational FunctionsChapter 3.7 - Polynomial And Rational InequalitiesChapter 4 - Exponential And Logarithmic FunctionsChapter 4.1 - Exponential FunctionsChapter 4.2 - The Natural Exponential FunctionChapter 4.3 - Logarithmic FunctionsChapter 4.4 - Laws Of LogarithmsChapter 4.5 - Exponential And Logarithmic EquationsChapter 4.6 - Modeling With Exponential FunctionsChapter 4.7 - Logarithmic ScalesChapter 5 - Trigonometric Functions: Unit Circle ApproachChapter 5.1 - The Unit CircleChapter 5.2 - Trigonometric Functions Of Real NumbersChapter 5.3 - Trigonometric GraphsChapter 5.4 - More Trigonometric GraphsChapter 5.5 - Inverse Trigonometric Functions And Their GraphsChapter 5.6 - Modeling Harmonic MotionChapter 6 - Trigonometric Functions: Right Triangle ApproachChapter 6.1 - Angle MeasureChapter 6.2 - Trigonometry Of Right TrianglesChapter 6.3 - Trigonometric Functions Of AnglesChapter 6.4 - Inverse Trigonometric Functions And Right TrianglesChapter 6.5 - The Law Of SinesChapter 6.6 - The Law Of CosinesChapter 7 - Analytic TrigonometryChapter 7.1 - Trigonometric IdentitiesChapter 7.2 - Addition And Subtraction FormulasChapter 7.3 - Double-angle, Half-angle, And Product-sum FormulasChapter 7.4 - Basic Trigonometric EquationsChapter 7.5 - More Trigonometric EquationsChapter 8 - Polar Coordinates And Parametric EquationsChapter 8.1 - Polar CoordinatesChapter 8.2 - Graphs Of Polar EquationsChapter 8.3 - Polar Form Of Complex Numbers; De Moivre's TheoremChapter 8.4 - Plane Curves And Parametric EquationsChapter 9 - Vectors In Two And Three DimensionsChapter 9.1 - Vectors In Two DimensionsChapter 9.2 - The Dot ProductChapter 9.3 - Three-dimensional Coordinate GeometryChapter 9.4 - Vectors In Three DimensionsChapter 9.5 - The Cross ProductChapter 9.6 - Equations Of Lines And PlanesChapter 10 - Systems Of Equations And InequalitiesChapter 10.1 - Systems Of Linear Equations In Two VariablesChapter 10.2 - Systems Of Linear Equations In Several VariablesChapter 10.3 - Matrices And Systems Of Linear EquationsChapter 10.4 - The Algebra Of MatricesChapter 10.5 - Inverses Of Matrices And Matrix EquationsChapter 10.6 - Determinants And Cramer's RuleChapter 10.7 - Partial FractionsChapter 10.8 - Systems Of Nonlinear EquationsChapter 10.9 - Systems Of InequalitiesChapter 11 - Conic SectionsChapter 11.1 - ParabolasChapter 11.2 - EllipsesChapter 11.3 - HyperbolasChapter 11.4 - Shifted ConicsChapter 11.5 - Rotation Of AxesChapter 11.6 - Polar Equations Of ConicsChapter 12 - Sequences And SeriesChapter 12.1 - Sequences And Summation NotationChapter 12.2 - Arithmetic SequencesChapter 12.3 - Geometric SequencesChapter 12.4 - Mathematics Of FinanceChapter 12.5 - Mathematical InductionChapter 12.6 - The Binomial TheoremChapter 13 - Limits: A Preview Of CalculusChapter 13.1 - Finding Limits Numerically And GraphicallyChapter 13.2 - Finding Limits AlgebraicallyChapter 13.3 - Tangent Lines And DerivativesChapter 13.4 - Limits At Infinity; Limits Of SequencesChapter 13.5 - Areas
Book Details
This bestselling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, providing students with a solid foundation in the principles of mathematical thinking. Comprehensive and evenly paced, the book provides complete coverage of the function concept, and integrates a significant amount of graphing calculator material to help students develop insight into mathematical ideas. The authors' attention to detail and clarity--the same as found in James Stewart's market-leading Calculus text--is what makes this text the proven market leader.
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