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Math
Calculus
Calculus: Early Transcendentals, Enhanced Etext
Chapter 14.7, Problem 11ES
Chapter 14.7, Problem 11ES
BUY
Calculus: Early Transcendentals, Enhanced Etext
12th Edition
ISBN:
9781119777984
Author: Howard Anton; Irl C. Bivens; Stephen Davis
Publisher:
Wiley Global Education US
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1 Limits And Continuity
2 The Derivative
3 Topics In Differentiation
4 The Derivative In Graphing And Applications
5 Integration
6 Applications Of The Definite Integral In Geometry, Science, And Engineering
7 Principles Of Integral Evaluation
8 Mathematical Modeling With Differential Equations
9 Infinite Series
10 Parametric And Polar Curves; Conic Sections
11 Three-dimensional Space; Vectors
12 Vector-valued Functions
13 Partial Derivatives
14 Multiple Integrals
15 Topics In Vector Calculus
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14.1 Double Integrals
14.2 Double Integrals Over Nonrectangular Regions
14.3 Double Integrals In Polar Coordinates
14.4 Surface Area; Parametric Surfaces
14.5 Triple Integrals
14.6 Triple Integrals In Cylindrical And Spherical Coordinates
14.7 Change Of Variables In Multiple Integrals; Jacobians
14.8 Centers Of Gravity Using Multiple Integrals
Chapter Questions
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Problem 1QCE: Let T be the transformation from the u-plane to the xy-plane defined by the equations x=u2,y=3u+ (a)...
Problem 2QCE: State the relationship between R and S in the change of variables formula...
Problem 3QCE
Problem 4QCE: The Jacobian of the transformation x=u,y=w,z=2w is x,y,zu,,w=
Problem 1ES: Find the Jacobian x,y/u,. x=u+4,y=3u5
Problem 2ES: Find the Jacobian x,y/u,. x=u+22,y=2u2
Problem 3ES
Problem 4ES: Find the Jacobian x,y/u,. x=2uu2+2,y=2u2+2
Problem 5ES: Solve for x and y in terms of uand, and then find the Jacobian x,y/u,. u=2x5y,=x+2y
Problem 6ES
Problem 7ES
Problem 8ES
Problem 9ES: Find the Jacobian x,y,z/u,,w. x=3u+,y=u2w,z=+w
Problem 10ES: Find the Jacobian x,y,z/u,,w. x=uu,y=uuw,z=uw
Problem 11ES
Problem 12ES
Problem 13ES: Determine whether the statement is true or false. Explain your answer. If r=xu,i+yu,j, then...
Problem 14ES
Problem 15ES
Problem 16ES
Problem 17ES: Sketch the image in the xy-plane of the set S under the given transformation.
Problem 18ES
Problem 19ES: Sketch the image in the xy-plane of the set S under the given transformation.
Problem 20ES: Sketch the image in the xy-plane of the set S under the given transformation.
Problem 21ES: Use the transformation u=x2y,=2x+y to find Rx2y2x+ydA where R is the rectangular region enclosed by...
Problem 22ES: Use the transformation u=x+y,=xy to find Rxyex2y2dA over the rectangular region R enclosed by the...
Problem 23ES
Problem 24ES
Problem 25ES: The transformation x=au,y=ba0,b0 can be rewritten as x/a=u,y/b=, and hence it maps the circular...
Problem 26ES
Problem 27ES: The transformation x=au,y=ba0,b0 can be rewritten as x/a=u,y/b=, and hence it maps the circular...
Problem 28ES: Show that the area of the ellipse x2a2+y2b2=1 is ab.
Problem 29ES: If a, b, and c are positive constants, then the transformation x=au,y=b,z=cw can be rewritten as...
Problem 30ES
Problem 31ES: Find a transformation u=fx,y,=gx,y that when applied to the region R in the xy-plane has as its...
Problem 32ES: Find a transformation u=fx,y,=gx,y that when applied to the region R in the xy-plane has as its...
Problem 33ES: Find a transformation u=fx,y,=gx,y that when applied to the region R in the xy-plane has as its...
Problem 34ES: Find a transformation u=fx,y,=gx,y that when applied to the region R in the xy-plane has as its...
Problem 35ES
Problem 36ES: Evaluate the integral by making an appropriate change of variables. Rx2y2dA, where R is the...
Problem 37ES: Evaluate the integral by making an appropriate change of variables. Rsinxycosx+ydA, where R is the...
Problem 38ES: Evaluate the integral by making an appropriate change of variables. Reyx/y+xdA, where R is the...
Problem 39ES: Use an appropriate change of variables to find the area of the region in the first quadrant enclosed...
Problem 40ES: Use an appropriate change of variables to find the volume of the solid bounded above by the plane...
Problem 41ES: Use the transformation u=x,=zy,w=xy to find Gzy2xydV where G is the region enclosed by the surfaces...
Problem 42ES: Use the transformation u=xy,=yz,w=xz to find the volume of the region in the first octant that is...
Problem 43ES: (a) Verify that a1b1c1d1a2b2c2d2=a1a2+b1c2a1b2+b1d2c1a2+d1c2c1b2+d1d2 (b) If x=xu,,y=yu, is a...
Problem 44ES: The formula obtained in part (b) of Exercise 43 is useful in integration problems where it is...
Problem 45ES: The formula obtained in part (b) of Exercise 43 is useful in integration problems where it is...
Problem 46ES: The formula obtained in part (b) of Exercise 43 is useful in integration problems where it is...
Problem 47ES: The three-variable analog of the formula derived in part (b) of Exercise 43 is x,y,zu,,wu,,wx,y,z=1...
Problem 48ES: (a) Consider the transformation x=rcos,y=rsin,z=z from cylindrical to rectangular coordinates where...
Problem 49ES
Problem 50ES
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