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Multivariable Calculus

8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781305266643

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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 3E:

Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...

Problem 4E:

Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...

Problem 5E:

(a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...

Problem 6E:

(a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...

Problem 7E:

(a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...

Problem 8E:

(a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...

Problem 9E:

(a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...

Problem 10E:

(a) 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 14E:

(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 16E:

(a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and...

Problem 17E:

(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 24E:

Match the graphs of the parametric equations x = f(t) and y = g(t) in (a)(d) with the parametric...

Problem 25E:

Use the graphs of x = f(t) and y = g(t) to sketch the parametric curve x = f(t), y = g(t). Indicate...

Problem 26E:

Use the graphs of x = f(t) and y = g(t) to sketch the parametric curve x = f(t), y = g(t). Indicate...

Problem 27E:

Use the graphs of x = f(t) and y = g(t) to sketch the parametric curve x = f(t), y = g(t). Indicate...

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 38E:

Compare the curves represented by the parametric equations. How do they differ? 38. (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 43E:

A curve, called a witch of Maria Agnesi, consists of all possible positions of the point P in the...

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 46E:

If a projectile is fired with an initial velocity of v0 meters per second at an angle above the...

Problem 47E:

Investigate the family of curves defined by the parametric equations x = t2, y = t3 ct. How does...

Problem 48E:

The swallowtail catastrophe curves ate defined by the parametric equations x = 2ct 4t3, y = ct2 +...

Problem 49E:

Graph several members of the family of curves with parametric equations x = t + a cos t, y = t + a...

Problem 50E:

Graph several members of the family of curves x = sin t + sin nt, y = cos t + cos nt, where n is a...

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

Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With MULTIVARIABLE CALCULUS, Eighth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course.

We offer sample solutions for Multivariable Calculus homework problems. See examples below:

(a) What is a parametric curve? (b) How do you sketch a parametric curve?(a) What is a convergent sequence? (b) What is a convergent series? (c) What does limn an = 3 mean?...What is the difference between a vector and a scalar?What is a vector function? How do you find its derivative and its integral?(a) What is a function of two variables? (b) Describe three methods for visualizing a function of...Evaluate the integral E(xy+z2)dv, where E=(x,y,z)0x2,0y1,0z3 using three different orders of...Suppose f is a continuous function defined on a rectangle R = [a, b] [c, d]. (a) Write an...What is a vector field? Give three examples that have physical meaning.(a) Write the general form of a second-order homogeneous linear differential equation with constant...

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