Essential Calculus2nd EditionStewart, James Publisher: Cengage LearningISBN: 9781133490975
Essential Calculus
Solutions for Essential Calculus
Problem 2E:
If f(x)=x2xx1andg(x)=x is it true that f = g?Problem 3E:
The graph of a function f is given. (a) State the value of f(1). (b) Estimate the value of f(1). (c)...Problem 4E:
The graphs of f and g are given. (a) State the values of f(4) and g(3). (b) For what values of x is...Problem 6E:
Determine whether the curve is the graph of a function of x. If it is, state the domain and range of...Problem 7E:
Determine whether the curve is the graph of a function of x. If it is, state the domain and range of...Problem 8E:
Determine whether the curve is the graph of a function of x. If it is, state the domain and range of...Problem 10E:
The graph shows the height of the water in a bathtub as a function of time. Give a verbal...Problem 12E:
Sketch a rough graph of the number of hours of daylight as a function of the time of year.Problem 14E:
Sketch a rough graph of the market value of a new car as a function of time for a period of 20...Problem 16E:
You place a frozen pie in an oven and bake it for an hour. Then you take it out and let it cool...Problem 17E:
A homeowner mows the lawn every Wednesday afternoon. Sketch a rough graph of the height of the grass...Problem 18E:
An airplane takes off from an airport and lands an hour later at another airport, 400 miles away. If...Problem 19E:
If f(x) = 3x2 x + 2, find f(2), f(2), f(a), f(a), f(a + 1), 2f(a), f(2a), f(a2), [f(a)]2, and f(a +...Problem 20E:
A spherical balloon with radius r inches has volume V(r)=43r3. Find a function that represents the...Problem 23E:
Evaluate the difference quotient for the given function. Simplify your answer. 29. f(x)=1x,...Problem 25E:
Find the domain of the function. 31. f(x)=x+4x29Problem 27E:
Find the domain of the function. 37. F(p)=2pProblem 43E:
Find an expression for the function whose graph is the given curve. 51. The line segment joining the...Problem 48E:
Find a formula for the described function and state its domain. 58. A rectangle has area 16 m2....Problem 50E:
Find a formula for the described function and state its domain. Express the surface area of a cube...Problem 51E:
Find a formula for the described function and state its domain. 61. An open rectangular box with...Problem 52E:
A cell phone plan has a basic charge of 35 a month. The plan includes 400 free minutes and charges...Problem 53E:
In a certain country, income tax is assessed as follows. There is no tax on income up to10,000. Any...Problem 54E:
The functions in Example 6 and Exercises 52 and 53(a) are called step functions because their graphs...Problem 55E:
Graphs of f and g are shown. Decide whether each function is even, odd, or neither. Explain your...Problem 56E:
Graphs of f and g are shown. Decide whether each function is even, odd, or neither. Explain your...Problem 57E:
(a) If the point (5, 3) is on the graph of an even function, what other point must also be on the...Problem 58E:
A function f has domain [5, 5] and a portion of its graph is shown. (a) Complete the graph of f if...Problem 59E:
Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...Problem 60E:
Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...Problem 61E:
Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...Problem 62E:
Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...Problem 63E:
Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...Problem 64E:
Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...Browse All Chapters of This Textbook
Chapter T - Diagnostic TestsChapter 1 - Functions And LimitsChapter 1.1 - Functions And Their RepresentationChapter 1.2 - A Catalog Of Essential FunctionsChapter 1.3 - The Limit Of A FunctionChapter 1.4 - Calculating LimitsChapter 1.5 - ContinuityChapter 1.6 - Limits Involving InfinityChapter 2 - DerivativesChapter 2.1 - Derivatives And Rates Of Change
Chapter 2.2 - The Derivative As A FunctionChapter 2.3 - Basic Differentiation FormulasChapter 2.4 - The Product And Quotient RulesChapter 2.5 - The Chain RuleChapter 2.6 - Implicit DifferentiationChapter 2.7 - Related RatesChapter 2.8 - Linear Approximation And DifferentialsChapter 3 - Inverse Functions: Exponential, Logarithmic, And Inverse Trigonometric FunctionsChapter 3.1 - Exponential FunctionsChapter 3.2 - Inverse Functions And LogarithmsChapter 3.3 - Derivatives Of Logarithmic And Exponential FunctionsChapter 3.4 - Exponential Growth And DecayChapter 3.5 - Inverse Trigonometric FunctionsChapter 3.6 - Hyperbolic FunctionsChapter 3.7 - Indeterminate Forms And L'hospital's RuleChapter 4 - Applications Of DifferentiationChapter 4.1 - Maximum And Minimum ValuesChapter 4.2 - The Mean Value TheoremChapter 4.3 - Derivatives And The Shapes Of GraphsChapter 4.4 - Curve SketchingChapter 4.5 - Optimization ProblemChapter 4.6 - Newton's MethodChapter 4.7 - AntiderivativesChapter 5 - IntegralsChapter 5.1 - Areas And DistancesChapter 5.2 - The Definite IntegralChapter 5.3 - Evaluating Definite IntegralsChapter 5.4 - The Fundamental Theorem Of CalculusChapter 5.5 - The Substitution RuleChapter 6 - Techniques Of IntegrationChapter 6.1 - Integration By PartsChapter 6.2 - Trigonometric Integrals And SubstitutionChapter 6.3 - Partial FractionsChapter 6.4 - Integration With Tables And Computer Algebra SystemsChapter 6.5 - Approximate IntegrationChapter 6.6 - Improper IntegralsChapter 7 - Applications Of IntegrationChapter 7.1 - Areas Between CurvesChapter 7.2 - VolumesChapter 7.3 - Volumes By Cylindrical ShellsChapter 7.4 - Arc LengthChapter 7.5 - Area Of A Surface Of RevolutionChapter 7.6 - Applications To Physics And EngineeringChapter 7.7 - Differential EquationsChapter 8 - SeriesChapter 8.1 - SequencesChapter 8.2 - SeriesChapter 8.3 - The Integral And Comparison TestsChapter 8.4 - Other Convergence TestsChapter 8.5 - Power SeriesChapter 8.6 - Representing Functions As Power SeriesChapter 8.7 - Taylor And Maclaurin SeriesChapter 8.8 - Applications Of Taylor PolynomialsChapter 9 - Parametric Equations And Polar CoordinatesChapter 9.1 - Parametric CurvesChapter 9.2 - Calculus With Parametric CurvesChapter 9.3 - Polar CoordinatesChapter 9.4 - Areas And Lengths In Polar CoordinatesChapter 9.5 - Conic Sections In Polar CoordinatesChapter 10 - Vectors And The Geometry Of SpaceChapter 10.1 - Three-dimensional Coordinate SystemsChapter 10.2 - VectorsChapter 10.3 - The Dot ProductChapter 10.4 - The Cross ProductChapter 10.5 - Equations Of Lines And PlanesChapter 10.6 - Cylinders And Quadratic SurfacesChapter 10.7 - Vector Functions And Space CurvesChapter 10.8 - Arc Length And CurvatureChapter 10.9 - Motion In Space: Velocity And AccelerationChapter 11 - Partial DerivativesChapter 11.1 - Functions Of Several VariablesChapter 11.2 - Limits And ContinuityChapter 11.3 - Partial DerivativesChapter 11.4 - Tangent Planes And Linear ApproximationsChapter 11.5 - The Chain RuleChapter 11.6 - Directional Derivatives And The Gradient VectorChapter 11.7 - Maximum And Minimum ValuesChapter 11.8 - Lagrange MultipliersChapter 12 - Multiple IntegralsChapter 12.1 - Double Integrals Over RectanglesChapter 12.2 - Double Integrals Over General RegionsChapter 12.3 - Double Integrals In Polar CoordinatesChapter 12.4 - Applications Of Double IntegralsChapter 12.5 - Triple IntegralsChapter 12.6 - Triple Integrals In Cylindrical CoordinatesChapter 12.7 - Triple Integrals In Spherical CoordinatesChapter 12.8 - Change Of Variables In Multiple IntegralsChapter 13 - Vector CalculusChapter 13.1 - Vector FieldsChapter 13.2 - Line IntegralsChapter 13.3 - The Fundamental Theorem For Line IntegralsChapter 13.4 - Green's TheoremChapter 13.5 - Curl And DivergenceChapter 13.6 - Parametric Surfaces And Their AreasChapter 13.7 - Surface IntegralsChapter 13.8 - Stokes' TheoremChapter 13.9 - The Divergence TheoremChapter A - TrigonometryChapter B - Sigma NotationChapter C - The Logarithm Defined As An Integral
Book Details
Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.
Sample Solutions for this Textbook
We offer sample solutions for Essential Calculus homework problems. See examples below:
Chapter T, Problem 1ADTA function f is defined as a ordered pair (x,f(x)) such that x and f(x) are related by a definite...Result used: Derivative rule: Let I be an interval, c∈I, and f:I→ℝ then f′(c)=limx→cf(x)−f(c)x−c...One to one function: When a function does not takes the same value twice, then the function is...Given: Distance between the point P from the track =1 Calculation: Two runners start at the point S...The Riemann sum of a function f is the method to find the total area underneath a curve. The area...Explanation to state the rule for integration by parts: The rule that corresponds to the Product...Consider the two curves y=f(x) and y=g(x). Here, the top curve function is f(x) and the bottom curve...Definition: If a sequence {an} has a limit l, then the sequence is convergent sequence, which can be...
The parametric curve is defined as the set of points (x,y) of the form x=f(t) and y=g(t), where...The difference between a vector and a scalar is explained in Table 1. Table 1 S No. Vector Scalar 1...Let the function be f(x,y) . The function of two variables is assigned by a two real numbers in ℝ2...Given that the continuous function f is defined on a rectangle R=[a,b]×[c,d]. The double integral of...Refer to Figure 1 in the textbook for the velocity vector fields showing San Francisco Bay wind...Formula used: The relation between degrees and radians is given by, π rad=180°. Calculation: Re...Definition used: If am,am+1,⋯,an are real numbers and m and n are integers such that m≤n, then...Definition used: The natural logarithmic function is the function defined by lnx=∫1x1tdt,x>0. If...
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