EBK MULTIVARIABLE CALCULUS8th EditionStewart Publisher: CENGAGE LISBN: 8220100807886
EBK MULTIVARIABLE CALCULUS
Solutions for EBK MULTIVARIABLE CALCULUS
Problem 1E:
Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...Problem 2E:
Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...Problem 11E:
(a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and...Problem 12E:
(a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and...Problem 13E:
(a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and...Problem 15E:
(a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and...Problem 18E:
(a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and...Problem 19E:
Describe the motion of a particle with position (x, y) as t varies in the given interval. 19. x = 5...Problem 20E:
Describe the motion of a particle with position (x, y) as t varies in the given interval. 20. x = 2...Problem 21E:
Describe the motion of a particle with position (x, y) as t varies in the given interval. 21. x = 5...Problem 22E:
Describe the motion of a particle with position (x, y) as t varies in the given interval. 22. x =...Problem 23E:
Suppose a curve is given by the parametric equations x = f(t), y = g(t), where the range of f is [1,...Problem 28E:
Match the parametric equations with the graphs labeled IVI. Give reasons for your choices. (Do not...Problem 29E:
Graph the curve x = y 2 sin y.Problem 30E:
Graph the curves y = x3 4x and x = y3 4y and find their points of intersection correct to one...Problem 31E:
(a) Show that the parametric equations x=x1+(x2x1)ty=y1+(y2y1)t where 0 t 1, describe the line...Problem 32E:
Use a graphing device and the result of Exercise 31(a) to draw the triangle with vertices A(1, 1),...Problem 33E:
Find parametric equations for the path of a particle that moves along the circle x2 + (y 1)2 = 4 in...Problem 34E:
(a) Find parametric equations for the ellipse x2/a2 + y2/b2 = 1. [Hint: Modify the equations of the...Problem 37E:
Compare the curves represented by the parametric equations. How do they differ? 37. (a) x = t3, y =...Problem 39E:
Derive Equations 1 for the case /2 .Problem 40E:
Let P be a point at a distance d from the center of a circle of radius r. The curve traced out by P...Problem 41E:
If a and b are fixed numbers, find parametric equations for the curve that consists of all possible...Problem 42E:
If a and b are fixed numbers, find parametric equations for the curve that consists of all possible...Problem 44E:
(a) Find parametric equations for the set of all points P as shown in the figure such that |OP| =...Problem 45E:
Suppose that the position of one particle at time t is given by x1=3sinty1=2cost0t2 and the position...Problem 47E:
Investigate the family of curves defined by the parametric equations x = t2, y = t3 ct. How does...Problem 50E:
Graph several members of the family of curves x = sin t + sin nt, y = cos t + cos nt, where n is a...Browse All Chapters of This Textbook
Chapter 10 - Parametric Equations And Polar CoordinatesChapter 10.1 - Curves Defined By Parametric EquationsChapter 10.2 - Calculus With Parametric CurvesChapter 10.3 - Polar CoordinatesChapter 10.4 - Areas And Lengths In Polar CoordinatesChapter 10.5 - Conic SectionsChapter 10.6 - Conic Sections In Polar CoordinatesChapter 11 - Infinite Sequences And SeriesChapter 11.1 - SequencesChapter 11.2 - Series
Chapter 11.3 - The Integral Test And Estimates Of SumsChapter 11.4 - The Comparison TestsChapter 11.5 - Alternating SeriesChapter 11.6 - Absolute Convergence And The Ratio And Root TestsChapter 11.7 - Strategy For Testing SeriesChapter 11.8 - Power SeriesChapter 11.9 - Representations Of Functions As Power SeriesChapter 11.10 - Taylor And Maclaurin SeriesChapter 11.11 - Applications Of Taylor PolynomialsChapter 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 - Equations Of Lines And PlanesChapter 12.6 - Cylinders And Quadric SurfacesChapter 13 - Vector FunctionsChapter 13.1 - Vector Functions And Space CurvesChapter 13.2 - Derivatives And Integrals Of Vector FunctionsChapter 13.3 - Arc Length And CurvatureChapter 13.4 - Motion In Space: Velocity And AccelerationChapter 14 - Partial DerivativesChapter 14.1 - Functions Of Several VariablesChapter 14.2 - Limits And ContinuityChapter 14.3 - Partial DerivativesChapter 14.4 - Tangent Planes And Linear ApproximationsChapter 14.5 - The Chain RuleChapter 14.6 - Directional Derivatives And The Gradient VectorChapter 14.7 - Maximum And Minimum ValuesChapter 14.8 - Lagrange MultipliersChapter 15 - Multiple IntegralsChapter 15.1 - Double Integrals Over RectanglesChapter 15.2 - Double Integrals Over General RegionsChapter 15.3 - Double Integrals In Polar CoordinatesChapter 15.4 - Applications Of Double IntegralsChapter 15.5 - Surface AreaChapter 15.6 - Triple IntegralsChapter 15.7 - Triple Integrals In Cylindrical CoordinatesChapter 15.8 - Triple Integrals In Spherical CoordinatesChapter 15.9 - Change Of Variables In Multiple IntegralsChapter 16 - Vector CalculusChapter 16.1 - Vector FieldsChapter 16.2 - Line IntegralsChapter 16.3 - The Fundamental Theorem For Line IntegralsChapter 16.4 - Green's TheoremChapter 16.5 - Curl And DivergenceChapter 16.6 - Parametric Surfaces And Their AreasChapter 16.7 - Surface IntegralsChapter 16.8 - Stokes' TheoremChapter 16.9 - The Divergence TheoremChapter 17 - Second-order Differential EquationsChapter 17.1 - Second-order Linear EquationsChapter 17.2 - Nonhomogeneous Linear EquationsChapter 17.3 - Applications Of Second-order Differential EquationsChapter 17.4 - Series SolutionsChapter G - Complex Numbers
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