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Math
Calculus
Calculus: Early Transcendentals, Enhanced Etext
Chapter 15.7, Problem 40ES
Chapter 15.7, Problem 40ES
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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15.1 Vector Fields
15.2 Line Integrals
15.3 Independence Of Path; Conservative Vector Fields
15.4 Green’s Theorem
15.5 Surface Integrals
15.6 Applications Of Surface Integrals; Flux
15.7 The Divergence Theorem
15.8 Stokes’ Theorem
Chapter Questions
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Problem 1QCE: Let G be a solid whose surface is oriented outward by the unit normal n, and let Fx,y,z denote a...
Problem 2QCE: The outward flux of Fx,y,z=xi+yj+zk across any unit cube is .
Problem 3QCE: If Fx,y,z is the velocity vector field for a steady-state incompressible fluid flow, then a point at...
Problem 4QCE: If F(r)=cr3r is an inverse-square field, and if is a closed orientable surface that surrounds the...
Problem 1ES: Verify Formula (1) in the Divergence Theorem by evaluating the surface integral and the triple...
Problem 2ES
Problem 3ES: Verify Formula (1) in the Divergence Theorem by evaluating the surface integral and the triple...
Problem 4ES: Verify Formula (1) in the Divergence Theorem by evaluating the surface integral and the triple...
Problem 5ES: Determine whether the statement is true or false. Explain your answer. The Divergence Theorem...
Problem 6ES
Problem 7ES
Problem 8ES: Determine whether the statement is true or false. Explain your answer. Since the divergence of an...
Problem 9ES: Use the Divergence Theorem to find the flux of F across the surface with outward orientation....
Problem 10ES: Use the Divergence Theorem to find the flux of F across the surface with outward orientation....
Problem 11ES: Use the Divergence Theorem to find the flux of F across the surface with outward orientation....
Problem 12ES: Use the Divergence Theorem to find the flux of F across the surface with outward orientation....
Problem 13ES: Use the Divergence Theorem to find the flux of F across the surface with outward orientation....
Problem 14ES
Problem 15ES: Use the Divergence Theorem to find the flux of F across the surface with outward orientation....
Problem 16ES: Use the Divergence Theorem to find the flux of F across the surface with outward orientation....
Problem 17ES: Use the Divergence Theorem to find the flux of F across the surface with outward orientation....
Problem 18ES
Problem 19ES: Use the Divergence Theorem to find the flux of F across the surface with outward orientation....
Problem 20ES: Prove that if r=xi+yj+zkand is the surface of a solid G oriented by outward unit normal, then...
Problem 21ES
Problem 22ES: Let Fx,y,z=ai+bj+ck be a constant vector field and let be the surface of a solid G. Use the...
Problem 23ES: Find a vector field Fx,y,z that has (a) positive divergence everywhere (b) negative divergence...
Problem 24ES: Let Fx,y,z be a nonzero vector field in 3-space whose component functions have continuous first...
Problem 25ES: Does the result in Exercise 25 remain true if the sphere is replaced by a cube? Explain.
Problem 26ES: Prove the identity, assuming that F, , and G satisfy the hypotheses of the Divergence Theorem and...
Problem 27ES: Prove the identity, assuming that F, , and G satisfy the hypotheses of the Divergence Theorem and...
Problem 28ES: Prove the identity, assuming that F, , and G satisfy the hypotheses of the Divergence Theorem and...
Problem 29ES: Prove the identity, assuming that F, , and G satisfy the hypotheses of the Divergence Theorem and...
Problem 30ES: Prove the identity, assuming that F, , and G satisfy the hypotheses of the Divergence Theorem and...
Problem 31ES: Use the Divergence Theorem to find all positive values of k such that Fr=rrk satisfies the condition...
Problem 32ES: Determine whether the vector field Fx,y,z is free of sources and sinks. If it is not, locate them....
Problem 33ES: Determine whether the vector field Fx,y,z is free of sources and sinks. If it is not, locate them....
Problem 34ES
Problem 35ES: Determine whether the vector field Fx,y,z is free of sources and sinks. If it is not, locate them....
Problem 36ES: Let be the surface of the solid G that is enclosed by the paraboloid z=1x2y2 and the plane z=0. Use...
Problem 37ES
Problem 38ES
Problem 39ES
Problem 40ES
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