Essential Calculus2nd EditionStewart, James Publisher: Cengage LearningISBN: 9781133490975
Essential Calculus
Solutions for Essential Calculus
Problem 1E:
If a ball is thrown into the air with a velocity of 40 ft/s, its height in feet t seconds later is...Problem 2E:
If a rock is thrown upward on the planet Mars with a velocity of 10 m/ s, its height in meters t...Problem 3E:
Use the given graph of f to state the value of each quantity, if it exists. If it does not exist,...Problem 4E:
For the function f whose graph is given, state the value of each quantity, if it exists. If it does...Problem 10E:
Sketch the graph of an example of a function f that satisfies all of the given conditions....Problem 12E:
Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct...Problem 14E:
Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct...Problem 30E:
Prove the statement using the , definition of a limit and illustrate with a diagram like Figure 15....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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