ELEM LINEAR ALGB 12E AC\LL12th EditionAnton Publisher: WILEYISBN: 9781119498889
ELEM LINEAR ALGB 12E AC\LL
Solutions for ELEM LINEAR ALGB 12E AC\LL
Problem 1QCE:
The function y=12x has domain and range .Problem 2QCE:
The function has domain and range .
Problem 1ES:
Simplify the expression without using a calculating utility. (a) 82/3 (b) 82/3 (c) 82/3Problem 3ES:
Use a calculating utility to approximate the expression. Round your answer to four decimal places....Problem 5ES:
Find the exact value of the expression without using a calculating utility. (a) log216 (b) log2132...Problem 7ES:
Use a calculating utility to approximate the expression. Round your answer to four decimal places....Problem 9ES:
Use the logarithm properties in Theorem 1.8.3 to rewrite the expression in terms of r,s, and t,...Problem 11ES:
Expand the logarithm in terms of sums, differences, and multiples of simpler logarithms. (a)...Problem 19ES:
Solve for x without using a calculating utility. ln1/x=2Problem 24ES:
Solve for x without using a calculating utility. Use the natural logarithm anywhere that logarithms...Problem 25ES:
Solve for x without using a calculating utility. Use the natural logarithm anywhere that logarithms...Problem 26ES:
Solve for x without using a calculating utility. Use the natural logarithm anywhere that logarithms...Problem 27ES:
Solve for x without using a calculating utility. Use the natural logarithm anywhere that logarithms...Problem 28ES:
Solve for x without using a calculating utility. Use the natural logarithm anywhere that logarithms...Problem 29ES:
Solve for x without using a calculating utility. Use the natural logarithm anywhere that logarithms...Problem 31ES:
In each part, identify the domain and range of the function, and then sketch the graph of the...Problem 33ES:
In each part, identify the domain and range of the function, and then sketch the graph of the...Problem 35ES:
Determine whether the statement is true or false. Explain your answer. The function y=x3 is an...Problem 36ES:
Determine whether the statement is true or false. Explain your answer. The graph of the exponential...Problem 37ES:
Determine whether the statement is true or false. Explain your answer. The natural logarithm...Problem 38ES:
Determine whether the statement is true or false. Explain your answer. The domain of a logarithmic...Problem 40ES:
Graph the functions on the same screen of a graphing utility. [Use the change of base formula 9 ,...Problem 41ES:
Graph the functions on the same screen of a graphing utility. [Use the change of base formula 9 ,...Problem 42ES:
(a) Derive the general change of base formula logbx=logaxlogab (b) Use the result in part (a) to...Problem 44ES:
Use a graphing utility to estimate the two points of intersection of the graphs of y=0.6x2 and...Problem 45ES:
(a) Is the curve in the accompanying figure the graph of an exponential function? Explain your...Problem 46ES:
(a) Make a conjecture about the general shape of the graph of y=loglogx, and sketch the graph of...Problem 47ES:
Find the fallacy in the following “proof� that 1814 . Multiply both sides of the inequality 32...Problem 50ES:
Find the limits. limx+1ex1+exProblem 51ES:
Find the limits. limx+ex+exexexProblem 53ES:
Find the limits. limx+ln2x2Problem 55ES:
Find the limits. limx+x+1xxxProblem 56ES:
Find the limits. limx+1+1xxProblem 57ES:
Evaluate the limit using an appropriate substitution. (See Exercises 45-46 of Section 1.3.)...Problem 58ES:
Evaluate the limit using an appropriate substitution. (See Exercises 45-46 of Section 1.3.)...Problem 61ES:
Evaluate the limit using an appropriate substitution. (See Exercises 45-46 of Section 1.3.)...Problem 62ES:
Evaluate the limit using an appropriate substitution. (See Exercises 45-46 of Section 1.3.)...Problem 63ES:
Evaluate the limit using an appropriate substitution. (See Exercises 45-46 of Section 1.3.)...Problem 65ES:
Let fx=bx, where 0b . Use the substitution principle to verify the asymptotic behavior of f that is...Problem 66ES:
Prove that limx01+x1/x=e by completing parts (a) and (b). (a) Use Equation 4 and the substitution...Problem 67ES:
Suppose that the speed (in ft/s) of a skydiver t second after leaping form a plane is given by the...Problem 68ES:
The population p of the United States (in millions) in year t can be modelled by the function...Problem 70ES:
Let fx=1+1xx . (a) Prove the identity fx=xx1fx1 (b) Use Equation (d) and the identity form part (a)...Problem 71ES:
If equipment in the satellite of Example 3 requires 15 watts to operate correctly, what is the...Problem 72ES:
The equation Q=12e0.055t gives the mass Q in grams of radioactive potassium-42 that will remain from...Problem 73ES:
The acidity of a substance is measured by its pH value, which is defined by the formula pH=logH+...Problem 74ES:
Use the definition of pH in Exercise 73 to find H+ in a solution having a pH equal to (a) 2.44 (b)...Problem 75ES:
The perceived loudness of a sound in decibels dB is related to its intensity I in watts per square...Problem 76ES:
Use the definition of the decibel level of a sound (see Exercise 75). If one sound is three times as...Problem 77ES:
Use the definition of the decibel level of a sound (see Exercise 75). According to one source, the...Problem 78ES:
Use the definition of the decibel level of a sound (see Exercise 75). Suppose that the intensity...Browse All Chapters of This Textbook
Chapter 1 - Limits And ContinuityChapter 1.1 - Limits (an Intuitive Approach)Chapter 1.2 - Computing LimitsChapter 1.3 - Limits At Infinity; End Behavior Of A FunctionChapter 1.4 - Limits (discussed More Rigorously)Chapter 1.5 - ContinuityChapter 1.6 - Continuity Of Trigonometric FunctionsChapter 1.7 - Inverse Trigonometric FunctionsChapter 1.8 - Exponential And Logarithmic FunctionsChapter 2 - The Derivative
Chapter 2.1 - Tangent Lines And Rates Of ChangeChapter 2.2 - The Derivative FunctionChapter 2.3 - Introduction To Techniques Of DifferentiationChapter 2.4 - The Product And Quotient RulesChapter 2.5 - Derivatives Of Trigonometric FunctionsChapter 2.6 - The Chain RuleChapter 3 - Topics In DifferentiationChapter 3.1 - Implicit DifferentiationChapter 3.2 - Derivatives Of Logarithmic FunctionsChapter 3.3 - Derivatives Of Exponential And Inverse Trigonometric FunctionsChapter 3.4 - Related RatesChapter 3.5 - Local Linear Approximation; DifferentialsChapter 3.6 - L’hôpital’s Rule; Indeterminate FormsChapter 4 - The Derivative In Graphing And ApplicationsChapter 4.1 - Analysis Of Functions I: Increase, Decrease, And ConcavityChapter 4.2 - Analysis Of Functions Ii: Relative Extrema; Graphing PolynomialsChapter 4.3 - Analysis Of Functions Iii: Rational Functions, Cusps, And Vertical TangentsChapter 4.4 - Absolute Maxima And MinimaChapter 4.5 - Applied Maximum And Minimum ProblemsChapter 4.6 - Rectilinear MotionChapter 4.7 - Newton’s MethodChapter 4.8 - Rolle’s Theorem; Mean-value TheoremChapter 5 - IntegrationChapter 5.1 - An Overview Of The Area ProblemChapter 5.2 - The Indefinite IntegralChapter 5.3 - Integration By SubstitutionChapter 5.4 - The Definition Of Area As A Limit; Sigma NotationChapter 5.5 - The Definite IntegralChapter 5.6 - The Fundamental Theorem Of CalculusChapter 5.7 - Rectilinear Motion Revisited Using IntegrationChapter 5.8 - Average Value Of A Function And Its ApplicationsChapter 5.9 - Evaluating Definite Integrals By SubstitutionChapter 5.10 - Logarithmic And Other Functions Defined By IntegralsChapter 6 - Applications Of The Definite Integral In Geometry, Science, And EngineeringChapter 6.1 - Area Between Two CurvesChapter 6.2 - Volumes By Slicing; Disks And WashersChapter 6.3 - Volumes By Cylindrical ShellsChapter 6.4 - Length Of A Plane CurveChapter 6.5 - Area Of A Surface Of RevolutionChapter 6.6 - WorkChapter 6.7 - Moments, Centers Of Gravity, And CentroidsChapter 6.8 - Fluid Pressure And ForceChapter 6.9 - Hyperbolic Functions And Hanging CablesChapter 7 - Principles Of Integral EvaluationChapter 7.1 - An Overview Of Integration MethodsChapter 7.2 - Integration By PartsChapter 7.3 - Integrating Trigonometric FunctionsChapter 7.4 - Trigonometric SubstitutionsChapter 7.5 - Integrating Rational Functions By Partial FractionsChapter 7.6 - Using Computer Algebra Systems And Tables Of IntegralsChapter 7.7 - Numerical Integration; Simpson’s RuleChapter 7.8 - Improper IntegralsChapter 8 - Mathematical Modeling With Differential EquationsChapter 8.1 - Modeling With Differential EquationsChapter 8.2 - Separation Of VariablesChapter 8.3 - Slope Fields; Euler’s MethodChapter 8.4 - First-order Differential Equations And ApplicationsChapter 9 - Infinite SeriesChapter 9.1 - SequencesChapter 9.2 - Monotone SequencesChapter 9.3 - Infinite SeriesChapter 9.4 - Convergence TestsChapter 9.5 - The Comparison, Ratio, And Root TestsChapter 9.6 - Alternating Series; Absolute And Conditional ConvergenceChapter 9.7 - Maclaurin And Taylor PolynomialsChapter 9.8 - Maclaurin And Taylor Series; Power SeriesChapter 9.9 - Convergence Of Taylor SeriesChapter 9.10 - Differentiating And Integrating Power Series; Modeling With Taylor SeriesChapter 10 - Parametric And Polar Curves; Conic SectionsChapter 10.1 - Parametric Equations; Tangent Lines And Arc Length For Parametric CurvesChapter 10.2 - Polar CoordinatesChapter 10.3 - Tangent Lines, Arc Length, And Area For Polar CurvesChapter 10.4 - Conic SectionsChapter 10.5 - Rotation Of Axes; Second-degree EquationsChapter 10.6 - Conic Sections In Polar CoordinatesChapter 11 - Three-dimensional Space; VectorsChapter 11.1 - Rectangular Coordinates In 3-space; Spheres; Cylindrical SurfacesChapter 11.2 - VectorsChapter 11.3 - Dot Product; ProjectionsChapter 11.4 - Cross ProductChapter 11.5 - Parametric Equations Of LinesChapter 11.6 - Planes In 3-spaceChapter 11.7 - Quadric SurfacesChapter 11.8 - Cylindrical And Spherical CoordinatesChapter 12 - Vector-valued FunctionsChapter 12.1 - Introduction To Vector-valued FunctionsChapter 12.2 - Calculus Of Vector-valued FunctionsChapter 12.3 - Change Of Parameter; Arc LengthChapter 12.4 - Unit Tangent, Normal, And Binormal VectorsChapter 12.5 - CurvatureChapter 12.6 - Motion Along A CurveChapter 12.7 - Kepler’s Laws Of Planetary MotionChapter 13 - Partial DerivativesChapter 13.1 - Functions Of Two Or More VariablesChapter 13.2 - Limits And ContinuityChapter 13.3 - Partial DerivativesChapter 13.4 - Differentiability, Differentials, And Local LinearityChapter 13.5 - The Chain RuleChapter 13.6 - Directional Derivatives And GradientsChapter 13.7 - Tangent Planes And Normal VectorsChapter 13.8 - Maxima And Minima Of Functions Of Two VariablesChapter 13.9 - Lagrange MultipliersChapter 14 - Multiple IntegralsChapter 14.1 - Double IntegralsChapter 14.2 - Double Integrals Over Nonrectangular RegionsChapter 14.3 - Double Integrals In Polar CoordinatesChapter 14.4 - Surface Area; Parametric SurfacesChapter 14.5 - Triple IntegralsChapter 14.6 - Triple Integrals In Cylindrical And Spherical CoordinatesChapter 14.7 - Change Of Variables In Multiple Integrals; JacobiansChapter 14.8 - Centers Of Gravity Using Multiple IntegralsChapter 15 - Topics In Vector CalculusChapter 15.1 - Vector FieldsChapter 15.2 - Line IntegralsChapter 15.3 - Independence Of Path; Conservative Vector FieldsChapter 15.4 - Green’s TheoremChapter 15.5 - Surface IntegralsChapter 15.6 - Applications Of Surface Integrals; FluxChapter 15.7 - The Divergence TheoremChapter 15.8 - Stokes’ Theorem
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