- 7.1: Integrate f (x, y, z) = xyz along the following paths: (a) c(t) = (...
- 7.2: Compute the integral of f along the path c in each of the following...
- 7.3: Compute each of the following line integrals: (a) C(sin x) dy (cos ...
- 7.4: If F(x) is orthogonal to c (t) at each point on the curve x = c(t),...
- 7.5: Find the work done by the force F(x, y) = (x y)i + 2xyj in moving a...
- 7.6: A ring in the shape of the curve x + y = a is formed of thin wire w...
- 7.7: Find a parametrization for each of the following surfaces: (a) x + ...
- 7.8: Find the area of the surface defined by : (u, v) (x, y, z), where x...
- 7.9: Write a formula for the surface area of : (r, ) (x, y, z), where x ...
- 7.10: Suppose z = f (x, y) and ( f/x)2 + ( f/y)2 = c, c > 0. Show that th...
- 7.11: Compute the integral of f (x, y, z) = x2 + y2 + z2 over the surface...
- 7.12: Find S f dS in each of the following cases: (a) f (x, y, z) = x; S ...
- 7.13: Compute the integral of f (x, y, z) = xyz over the rectangle with v...
- 7.14: Compute the integral of x + y over the surface of the unit sphere.
- 7.15: Compute the surface integral of x over the triangle with vertices (...
- 7.16: A paraboloid of revolution S is parametrized by (u, v) = (u cos v, ...
- 7.17: Let f (x, y, z) = xey cos z. (a) Compute F = f . (b) Evaluate C F d...
- 7.18: Let F(x, y, z) = xi + yj + zk. Evaluate S F dS, where S is the uppe...
- 7.19: Let F(x, y, z) = xi + yj + zk. Evaluate c F ds, where c(t) = (et , ...
- 7.20: Let F = f for a given scalar function. Let c(t) be a closed curve, ...
- 7.21: Consider the surface (u, v) = (u cos v, u sin v, u). Compute the un...
- 7.22: Let S be the part of the cone z = x + y with z between 1 and 2 orie...
- 7.23: Let F = xi + xj + yzk represent the velocity field of a fluid (velo...
- 7.24: Show that the surface area of the part of the sphere x2 + y2 + z2 =...
- 7.25: Let S be a surface and C a closed curve bounding S. Verify the equa...
- 7.26: Calculate S F dS, where F(x, y, z) = (x, y, y) and S is the cylindr...
- 7.27: Let S be the portion of the cylinder x2 + y2 = 4 between the planes...
- 7.28: Let be the curve of intersection of the plane z = ax + by, with the...
- 7.29: A circular helix that lies on the cylinder x + y = R with pitch p m...
Solutions for Chapter 7: Integrals Over Paths and Surfaces
Full solutions for Vector Calculus | 6th Edition
ISBN: 9781429215084
Solutions for Chapter 7
13
5
Chapter 7: Integrals Over Paths and Surfaces includes 29 full step-by-step solutions. This textbook survival guide was created for the textbook: Vector Calculus, edition: 6. Since 29 problems in chapter 7: Integrals Over Paths and Surfaces have been answered, more than 13892 students have viewed full step-by-step solutions from this chapter. Vector Calculus was written by and is associated to the ISBN: 9781429215084. This expansive textbook survival guide covers the following chapters and their solutions.
Key Calculus Terms and definitions covered in this textbook
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Addition property of inequality
If u < v , then u + w < v + w
-
Average rate of change of ƒ over [a, b]
The number ƒ(b) - ƒ(a) b - a, provided a ? b.
-
Bounded below
A function is bounded below if there is a number b such that b ? ƒ(x) for all x in the domain of f.
-
Common ratio
See Geometric sequence.
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Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)
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Demand curve
p = g(x), where x represents demand and p represents price
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Directrix of a parabola, ellipse, or hyperbola
A line used to determine the conic
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Equilibrium price
See Equilibrium point.
-
Equivalent systems of equations
Systems of equations that have the same solution.
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Expanded form
The right side of u(v + w) = uv + uw.
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Geometric sequence
A sequence {an}in which an = an-1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.
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Mapping
A function viewed as a mapping of the elements of the domain onto the elements of the range
-
Polar form of a complex number
See Trigonometric form of a complex number.
-
Regression model
An equation found by regression and which can be used to predict unknown values.
-
Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt
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Vertex of an angle
See Angle.
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Vertical line
x = a.
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Weights
See Weighted mean.
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Window dimensions
The restrictions on x and y that specify a viewing window. See Viewing window.
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xz-plane
The points x, 0, z in Cartesian space.