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Math
Calculus
EBK CALCULUS EARLY TRANSCENDENTALS
Chapter 16.5, Problem 40E
Chapter 16.5, Problem 40E
BUY
EBK CALCULUS EARLY TRANSCENDENTALS
9th Edition
ISBN:
9780357687901
Author: Stewart
Publisher:
CENGAGE L
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1 Functions And Models
2 Limits And Derivatives
3 Differentiation Rules
4 Applications Of Differentiation
5 Integrals
6 Applications Of Integration
7 Techniques Of Integration
8 Further Applications Of Integration
9 Differential Equations
10 Parametric Equations And Polar Coordinates
11 Sequences, Series, And Power Series
12 Vectors And The Geometry Of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
A Numbers, Inequalities, And Absolute Values
B Coordinate Geometry And Lines
C Graphs Of Second-degree Equations
D Trigonometry
E Sigma Notation
F Proofs Of Theorems
G The Logarithm Defined As An Integral
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16.1 Vector Fields
16.2 Line Integrals
16.3 The Fundamental Theorem For Line Integrals
16.4 Green's Theorem
16.5 Curl And Divergence
16.6 Parametric Surfaces And Their Areas
16.7 Surface Integrals
16.8 Stokes' Theorem
16.9 The Divergence Theorem
16.10 Summary
Chapter Questions
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Problem 1E: Find (a) the curl and (b) the divergence of the vector field. 1. F(x, y, z) = xy2z2 i + x2yz2 j +...
Problem 2E: Find (a) the curl and (b) the divergence of the vector field. 2. F(x, y, z) = x3yz2 j + y4z3 k
Problem 3E: Find (a) the curl and (b) the divergence of the vector field. 3. F(x, y, z) = xyez i + yzex k
Problem 4E: Find (a) the curl and (b) the divergence of the vector field. 4. F (x, y, z) = sin yz i + sin zx j +...
Problem 5E: Find (a) the curl and (b) the divergence of the vector field. 5. x, y, z) = i + j + k
Problem 6E
Problem 7E: Find (a) the curl and (b) the divergence of the vector field. 7. F(x, y, z) = ex sin y, ey sin z, ez...
Problem 8E: Find (a) the curl and (b) the divergence of the vector field. 8. F(x, y, z) = arctan(xy),...
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E: (a) Verify Formula 3 for f(x,y,z)=sinxyz . (b) Verify Formula 11 for F(x,y,z)=xyz2i+x2yz3j+y2k .
Problem 14E: Let f be a scalar field and F a vector field. State whether each expression is meaningful. If not,...
Problem 15E: Determine whether or not the vector field is conservative. If it is conservative, find a function f...
Problem 16E: Determine whether or not the vector field is conservative. If it is conservative, find a function f...
Problem 17E: Determine whether or not the vector field is conservative. If it is conservative, find a function f...
Problem 18E: Determine whether or not the vector field is conservative. If it is conservative, find a function f...
Problem 19E: Determine whether or not the vector field is conservative. If it is conservative, find a function f...
Problem 20E
Problem 21E: Is there a vector field G on 3 such that curl G = x sin y, cos y, z xy? Explain.
Problem 22E: Is there a vector field G on 3 such that curl G = x, y, z? Explain.
Problem 23E: Show that any vector field of the form F(x, y, z) = f(x) i + g(y) j + h(z) k where f, g, h are...
Problem 24E: Show that any vector field of the form F(x, y, z) = f(y, z) i + g(x, z) j + h(x, y) k is...
Problem 25E: Prove the identity, assuming that the appropriate partial derivatives exist and are continuous. If f...
Problem 26E
Problem 27E: Prove the identity, assuming that the appropriate partial derivatives exist and are continuous. If f...
Problem 28E: Prove the identity, assuming that the appropriate partial derivatives exist and are continuous. If f...
Problem 29E: Prove the identity, assuming that the appropriate partial derivatives exist and are continuous. If f...
Problem 30E: Prove the identity, assuming that the appropriate partial derivatives exist and are continuous. If f...
Problem 31E: Prove the identity, assuming that the appropriate partial derivatives exist and are continuous. If f...
Problem 32E: Let r = x i + y j + z k and r = |r|. 30. Verify each identity. (a) r = 3 (b) (rr) = 4r (c) 2r3 =...
Problem 33E
Problem 34E: Let r = x i + y j + z k and r = |r|. 32. If F = r/rp, find div F. Is there a value of p for which...
Problem 35E: Use Greens Theorem in the form of Equation 13 to prove Greens first identity: Df2gdA=Cf(g)ndsDfgdA...
Problem 36E
Problem 37E
Problem 38E: Use Green's first identity to show that if f is harmonic on D , and if f(x,y)=0 on the boundary...
Problem 39E
Problem 40E
Problem 41E
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