Essential Calculus2nd EditionStewart, James Publisher: Cengage LearningISBN: 9781133490975
Essential Calculus
Solutions for Essential Calculus
Problem 1ADT:
Evaluate each expression without using a calculator. (a) (3)4 (b) 34 (c) 34 (d) 523521 (e) (23)2 (f)...Problem 2ADT:
Simplify each expression. Write your answer without negative exponents.
(3a3b3)(4ab2)2
Problem 4ADT:
Factor each expression.
4x2 − 25
2x2 + 5x − 12
x3 − 3x2 − 4x + 12
x4 + 27x
3x3/2 − 9x1/2 +...Problem 5ADT:
Simplify the rational expression.
Problem 6ADT:
Rationalize the expression and simplify.
(a)
(b)
Problem 8ADT:
Solve the equation. (Find only the real solutions.)
x + 5 = 14 −x
x2 − x − 12 = 0
2x2 + 4x +1 =...Problem 9ADT:
Solve each inequality. Write your answer using interval notation.
−4 < 5 − 3x ≤ 17
x2 < 2x + 8
x(x −...Problem 10ADT:
State whether each equation is true or false.
Problem 1BDT:
Find an equation for the line that passes through the point (2, 5) and (a) has slope 3 (b) is...Problem 4BDT:
Let A(−7, 4) and B(5, −12) be points in the plane.
Find the slope of the line that contains A and...Problem 5BDT:
Sketch the region in the xy-plane defined by the equation or inequalities.
−1 ≤ y ≤ 3
| x | < 4 and...Problem 1CDT:
The graph of a function f is given at the left. (a) State the value of f(1). (b) Estimate the value...Problem 4CDT:
How are graphs of the functions obtained from the graph of f? (a) y = f(x) (b) y = 2f(x) 1 (c) y =...Problem 5CDT:
Without using a calculator, make a rough sketch of the graph.
y = x3
y = (x + 1)3
y = (x − 2)3 +...Problem 6CDT:
Let
Evaluate f(−2) and f(1).
Sketch the graph of f.
Problem 2DDT:
Convert from radians to degrees. (a) 5/6 (b) 2Problem 3DDT:
Find the length of an arc of a circle with radius 12 cm if the arc subtends a central angle of...Problem 7DDT:
Prove the identities.
tan θ sin θ + cos θ = sec θ
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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