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Math
Calculus
Calculus, Early Transcendentals
Chapter 16.3, Problem 12E
Chapter 16.3, Problem 12E
BUY
Calculus, Early Transcendentals
9th Edition
ISBN:
9781337613927
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: The figure shows a curve C and a contour map of a function f whose gradient is continuous. Find C f...
Problem 2E: A table of values of a function f with continuous gradient is given. Find C f dr, where C has...
Problem 3E: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =...
Problem 4E: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =...
Problem 5E: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =...
Problem 6E: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =...
Problem 7E: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =...
Problem 8E: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =...
Problem 9E: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =...
Problem 10E: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =...
Problem 11E: The figure shows the vector field F(x, y) = 2xy, x2 and three curves that start at (1, 2) and end at...
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E: (a) Find a function f such that F = f and (b) use part (a) to evaluate C F dr along the given...
Problem 20E: (a) Find a function f such that F = f and (b) use part (a) to evaluate C F dr along the given...
Problem 21E
Problem 22E
Problem 23E
Problem 24E: (a) Find a function f such that F = f and (b) use part (a) to evaluate C F dr along the given...
Problem 25E: Show that the line integral is independent of path and evaluate the integral. 19. C 2xey dx + (2y ...
Problem 26E: Show that the line integral is independent of path and evaluate the integral. 20. C sin y dx + (x...
Problem 27E: Suppose youre asked to determine the curve that requires the least work for a force field F to move...
Problem 28E: Suppose an experiment determines that the amount of work required for a force field F to move a...
Problem 29E: Find the work done by the force field F in moving an object from P to Q. 23. F(x, y) = x3 i + y3 j;...
Problem 30E: Find the work done by the force field F in moving an object from P to Q. 24. F(x, y) = (2x + y) i +...
Problem 31E: Is the vector field shown in the figure conservative? Explain.
Problem 32E: Is the vector field shown in the figure conservative? Explain.
Problem 33E
Problem 34E: Let F = f, where f(x, y) = sin(x 2y). Find curves C1 and C2 that are not closed and satisfy the...
Problem 35E: Show that if the vector field F = P i + Q j + R k is conservative and P, Q, R have continuous...
Problem 36E
Problem 37E: Determine whether or not the given set is (a) open, (b) connected, and (c) simply-connected. 31....
Problem 38E: Determine whether or not the given set is (a) open, (b) connected, and (c) simply-connected. 32....
Problem 39E
Problem 40E: Determine whether or not the given set is (a) open, (b) connected, and (c) simply-connected. 34....
Problem 41E: Let F(x, y) = yi+xjx2+y2 (a) Show that P/y=Q/x. (b) Show that C F dr is not independent of path....
Problem 42E
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