EBK THOMAS'CALCULUS, EARLY TRANSCEND.14th EditionHass Publisher: PEARSONISBN: 9780134606095
EBK THOMAS'CALCULUS, EARLY TRANSCEND.
Solutions for EBK THOMAS'CALCULUS,EARLY TRANSCEND.
Problem 10GYR:
What formula do we need, in addition to the three listed in Question 9, to differentiate rational...Problem 12GYR:
What is the derivative of the exponential function ex? How does the domain of the derivative compare...Problem 83PE:
Find d2y/dx2 by implicit differentiation:
x3 + y3 = 1
Problem 99PE:
Tangent lines with specified slope Are there any points on the curve y = (x/2) + 1/(2x − 4) where...Problem 103PE:
Tangent lines perpendicular or parallel to lines Find the points on the curve y = 2x3 − 3x2 − 12x +...Problem 119PE:
Each of the figures in Exercises 119 and 120 shows two graphs, the graph of a function y = f(x)...Problem 125PE:
Find the limits in Exercises 125–132.
125.
Problem 127PE:
Find the limits in Exercises 125–132.
127.
Problem 131PE:
Find the limits in Exercises 125–132.
131.
Problem 135PE:
In Exercises 135–140, use logarithmic differentiation to find the derivative of y with respect to...Problem 137PE:
In Exercises 135–140, use logarithmic differentiation to find the derivative of y with respect to...Problem 139PE:
In Exercises 135–140, use logarithmic differentiation to find the derivative of y with respect to...Problem 143PE:
Circle’s changing area The radius r of a circle is changing at the rate of −2/π m/sec. At what rate...Problem 144PE:
Cube’s changing edges The volume of a cube is increasing at the rate of 1200 cm3/min at the instant...Problem 147PE:
Speed of moving particle The coordinates of a particle moving in the metric xy-plane are...Problem 148PE:
Motion of a particle A particle moves along the curve y = x3/2 in the first quadrant in such a way...Problem 149PE:
Draining a tank Water drains from the conical tank shown in the accompanying figure at the rate of 5...Problem 150PE:
Rotating spool As television cable is pulled from a large spool to be strung from the telephone...Problem 151PE:
Moving searchlight beam The figure shows a boat 1 km off-shore, sweeping the shore with a...Problem 153PE:
Find the linearizations of
tan x at x = −π/4
sec x at x = −π/4.
Graph the curves and linearizations...Problem 155PE:
Find the linearization of at x = 0.
Problem 157PE:
Surface area of a cone Write a formula that estimates the change that occurs in the lateral surface...Problem 159PE:
Compounding error The circumference of the equator of a sphere is measured as 10 cm with a possible...Problem 160PE:
Finding height To find the height of a lamppost (see accompanying figure), you stand a 6-ft pole 20...Problem 4AAE:
Solutions to differential equations
Show that y = sin x, y = cos x, and y = a cos x + b sin x (a and...Problem 10AAE:
Motion of a particle The position at time t ≥ 0 of a particle moving along a coordinate line is
s =...Problem 11AAE:
Shooting a paper clip On Earth, you can easily shoot a paper clip 64 ft straight up into the air...Problem 12AAE:
Velocities of two particles At time t sec, the positions of two particles on a coordinate line are...Problem 17AAE:
Find all values of the constants m and b for which the function
is
continuous at x =...Problem 22AAE:
Even differentiable functions Is there anything special about the derivative of an even...Problem 23AAE:
Suppose that the functions f and g are defined throughout an open interval containing the point x0,...Problem 24AAE:
(Continuation of Exercise 23.) Use the result of Exercise 23 to show that the following functions...Problem 25AAE:
Is the derivative of
continuous at x = 0? How about the derivative of k(x) = xh(x)? Give reasons...Browse All Chapters of This Textbook
Chapter 1 - FunctionsChapter 1.1 - Functions And Their GraphsChapter 1.2 - Combining Functions; Shifting And Scaling GraphsChapter 1.3 - Trigonometric FunctionsChapter 1.4 - Graphing With SoftwareChapter 1.5 - Exponential FunctionsChapter 1.6 - Inverse Functions And LogarithmsChapter 2 - Limits And ContinuityChapter 2.1 - Rates Of Change And Tangent Linea To CurvesChapter 2.2 - Limit Of A Function And Limit Laws
Chapter 2.3 - The Precise Definition Of A LimitChapter 2.4 - One-sided LimitsChapter 2.5 - ContinuityChapter 2.6 - Limits Involving Infinity; Asymptotes Of GraphsChapter 3 - DerivativesChapter 3.1 - Tangent Lines And The Derivative At A PointChapter 3.2 - The Derivative As A FunctionChapter 3.3 - Differentiation RulesChapter 3.4 - The Derivative As A Rate Of ChangeChapter 3.5 - Derivatives Of Trigonometric FunctionsChapter 3.6 - The Chain RuleChapter 3.7 - Implicit DifferentiationChapter 3.8 - Derivatives Of Inverse Functions And LogarithmsChapter 3.9 - Inverse Trigonometric FunctionsChapter 3.10 - Related RatesChapter 3.11 - Linearization And DifferentialsChapter 4 - Application Of DerivativesChapter 4.1 - Extreme Values Of Functions On Closed IntervalsChapter 4.2 - The Mean Value TheoremChapter 4.3 - Monotonic Functions And The First Derivative TestChapter 4.4 - Concavity And Curve SketchingChapter 4.5 - Indeterminate Forms And L'hopital's RuleChapter 4.6 - Applied OptimizationChapter 4.7 - Newton's MethodChapter 4.8 - AntiderivativesChapter 5 - IntegralsChapter 5.1 - Area And Estimating With Finite SumsChapter 5.2 - Sigma Notation And Limits Of Finite SumsChapter 5.3 - The Definite IntegralChapter 5.4 - The Fundamental Theorem Of CalculusChapter 5.5 - Indefinite Integrals And The Substitution MethodChapter 5.6 - Definite Integral Substitutions And The Area Between CurvesChapter 6 - Applications Of Definite IntegralsChapter 6.1 - Volumes Using Cross-sectionsChapter 6.2 - Volumes Using Cylindrical ShellsChapter 6.3 - Arc LengthChapter 6.4 - Areas Of Surfaces Of RevolutionChapter 6.5 - Work And Fluid ForcesChapter 6.6 - Moments And Centers Of MassChapter 7 - Integrals And Trascendental FunctionsChapter 7.1 - The Logarithm Defined As Ana IntegralChapter 7.2 - Exponential Change And Separable Differential EquationsChapter 7.3 - Hyperbolic FunctionsChapter 7.4 - Relative Rates Of GrowthChapter 8 - Techniques Of IntegrationChapter 8.1 - Using Basic Integration FormulasChapter 8.2 - Integration By PartsChapter 8.3 - Trigonometric IntegralsChapter 8.4 - Trigonometric SubstitutionsChapter 8.5 - Integration Of Rational Functions By Partial FractionsChapter 8.6 - Integral Tables And Computer Algebra SystemsChapter 8.7 - Numerical IntegrationChapter 8.8 - Improper IntegralsChapter 8.9 - ProbabilityChapter 9 - First-order Differential EquationsChapter 9.1 - Solutions, Slope Fields, And Euler's MethodChapter 9.2 - First-order Linear EquationsChapter 9.3 - ApplicationsChapter 9.4 - Graphical Solutions Of Autonomous EquationsChapter 9.5 - Systems Of Equations And Phase PlanesChapter 10 - Infinite Sequences And SeriesChapter 10.1 - SequencesChapter 10.2 - Infinite SeriesChapter 10.3 - The Integral TestChapter 10.4 - Comparison TestsChapter 10.5 - Absolute Convergence; The Ratio And Root TestsChapter 10.6 - Alternating Series And Conditional ConvergenceChapter 10.7 - Power SeriesChapter 10.8 - Taylor And Maclaurin SeriesChapter 10.9 - Convergence Of Taylor SeriesChapter 10.10 - Applications Of Taylor SeriesChapter 11 - Parametric Equations And Polar CoordinatesChapter 11.1 - Parametrizations Of Plane CurvesChapter 11.2 - Calculus With Parametric CurvesChapter 11.3 - Polar CoordinatesChapter 11.4 - Graphing Polar Coordinate EquationsChapter 11.5 - Areas And Lengths In Polar CoordinatesChapter 11.6 - Conic SectionsChapter 11.7 - Conics In Polar CoordinatesChapter 12 - Vectors And The Geometry Of SpaceChapter 12.1 - Three-dimensional Coordinate SystemsChapter 12.2 - VectorsChapter 12.3 - The Dot ProductChapter 12.4 - The Cross ProductChapter 12.5 - Lines And Planes In SpaceChapter 12.6 - Cylinders And Quadratic SurfacesChapter 13 - Vector-valued Functions And Motion In SpaceChapter 13.1 - Curves In Space And Their TangentsChapter 13.2 - Integrals Of Vector Functions; Projectile MotionChapter 13.3 - Arc Length In SpaceChapter 13.4 - Curvature And Normal Vectors Of A CurveChapter 13.5 - Tangential And Normal Vectors Of A Components Of AccelerationChapter 13.6 - Velocity And Acceleration In Polar CoordinatesChapter 14 - Partial DerivativesChapter 14.1 - Functions Of Several VariablesChapter 14.2 - Limits And Continuity In Higher DimensionsChapter 14.3 - Partial DerivativesChapter 14.4 - The Chain RuleChapter 14.5 - Directional Derivatives And Gradient VectorsChapter 14.6 - Tangent Planes And DifferentialsChapter 14.7 - Extreme Values And Saddle PointsChapter 14.8 - Lagrange MultipliersChapter 14.9 - Taylor's Formula For Two VariablesChapter 14.10 - Partial Derivatives With Constrained VariablesChapter 15 - Multiple IntegralsChapter 15.1 - Double And Iterated Integrals Over RectanglesChapter 15.2 - Double Integrals Over General RegionsChapter 15.3 - Area By Double IntegrationChapter 15.4 - Double Integrals In Polar FormChapter 15.5 - Triple Integrals In Rectangular CoordinatesChapter 15.6 - ApplicationsChapter 15.7 - Triple Integrals In Cylindrical And Spherical CoordinatesChapter 15.8 - Substitution In Multiple IntegralsChapter 16 - Integrals And Vector FieldsChapter 16.1 - Line Integrals Of Scalar FunctionsChapter 16.2 - Vector Fields And Line Integrals: Work, Circulation, And FluxChapter 16.3 - Path Independence, Conservative Fields, And Potential FunctionsChapter 16.4 - Green's Theorem In The PlaneChapter 16.5 - Surfaces And AreaChapter 16.6 - Surface IntegralsChapter 16.7 - Stokes' TheoremChapter 16.8 - The Divergence Theorem And A Unified TheoryChapter 17.1 - Second-order Linear EquationsChapter 17.2 - Nonhomogeneous Linear EquationsChapter 17.3 - ApplicationsChapter 17.4 - Euler EquationsChapter 17.5 - Power-series SolutionsChapter A.1 - Real Numbers And The Real LineChapter A.2 - Mathematical InductionChapter A.3 - Lines, Circles, And ParabolasChapter A.4 - Proofs Of Limit TheoremsChapter A.7 - Complex Numbers
Book Details
For three-semester or four-quarter courses in Calculus for students majoring in mathematics, engineering, or science Clarity and precision Thomas' Calculus: Early Transcendentals helps students reach the level of mathematical proficiency and maturity you
Sample Solutions for this Textbook
We offer sample solutions for EBK THOMAS'CALCULUS,EARLY TRANSCEND. homework problems. See examples below:
Function: A function is expressed in terms of dependent and independent variable. For every...Given information: The function is g(t). The interval from t=a to t=b. Calculation: Calculate the...Consider a function f is differentiable at a domain value a, then f′(a) is a real number. Then, the...According to the Extreme Value Theorem, If a function f(x) is continuous on a closed interval [a,...To find the area of the shaded region R that lies above the x-axis, below the graph of y=1−x2 and...The volume of a solid of integrable cross-sectional area A(x) from x=a to x=b is the integral of A...The natural logarithm is the function given by lnx=∫1x1tdt, x>0. The number e is the number in...Write the formula for integration by parts as below. ∫u(x)v′(x)dx=u(x)v(x)−∫v(x)u′(x)dx The...A first-order differential equation is of the form dydx=f(x,y) in which f(x,y) is a function of two...
The infinite sequence of numbers is a function whose domain is the set of positive integers....Description: Parametrization of the curve consists of both equations and intervals of a curve...Description: Generally, the vector is signified by the directed line segment PQ→ with initial point...Description: Rules for differentiating vector functions: Consider, u and v is the differentiable...Suppose D is a set of n-tuples of real numbers (x1, x2,…,xn). A real-valued function f on D is a...The double integral of a function of two variables f(x,y) over a region in the coordinate plane as...Calculation: Definition: If f is defined on a curve C given parametrically by...Formula used: Power Series Method: The power series method for solving a second-order homogenous...
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