 14.6.61E: Heat flux The heat flow vector field for conducting objects is F = ...
 14.6.62E: Heat flux The heat flow vector field for conducting objects is F = ...
 14.6.63E: Heat flux The heat flow vector field for conducting objects is F = ...
 14.6.64E: Flux across a cylinder Let S be the cylinder x2 + y2 = a2, for ?L ?...
 14.6.68E: Mass and center of mass Let S be a surface that represents a thin s...
 14.6.41E: Average values Find the average value of the function f(x, y, z) = ...
 14.6.69E: Mass and center of mass Let S be a surface that represents a thin s...
 14.6.70AE: Outward normal to a sphere Show that tu× tv  = a2 sin u for a sph...
 14.6.71AE: Special case of surface integrals of scalarvalued functionsSuppose...
 14.6.72AE: Surfaces of revolution Suppose y = f(x) is a continuous and positiv...
 14.6.73AE: Rain on roofs Let z = s(x, y) define a surface over a region R in t...
 14.6.74AE: Surface area of a torusa. Show that a torus with radii R > r (see f...
 14.6.22E: Surface area using a parametric description Find the area of the fo...
 14.6.21E: Surface area using a parametric description Find the area of the fo...
 14.6.65E: Flux across concentric spheres Consider the radial fields where p i...
 14.6.66E: Mass and center of mass Let S be a surface that represents a thin s...
 14.6.24E: Surface area using a parametric description Find the area of the fo...
 14.6.67E: Mass and center of mass Let S be a surface that represents a thin s...
 14.6.42E: Average values Find the average value of the temperature function T...
 14.6.43E: Surface integrals of vector fields Find the flux of the following v...
 14.6.19E: Identify the surface Describe the surface with the given parametric...
 14.6.1E: Give a parametric description for a cylinder with radius a and heig...
 14.6.2E: Give a parametric description for a cone with radius a and height h...
 14.6.3E: Give a parametric description for a sphere with radius a, including...
 14.6.4E: Explain how to compute the surface integral of a scalarvalued func...
 14.6.5E: Explain how to compute the surface integral of a scalarvalued func...
 14.6.6E: Explain how to compute a surface integral F · n dS valued 1 cone u...
 14.6.7E: Explain how to compute a surface integral F · n dS over a sphere us...
 14.6.8E: Explain what it means for a surface to be orientable.
 14.6.9E: Describe the usual orientation of a closed surface such as a sphere.
 14.6.10E: Why is the upward flux of a vertical vector field F = ?0, 0, 1 ? ac...
 14.6.11E: Parametric descriptions Give a parametric description of the form r...
 14.6.12E: Parametric descriptions Give a parametric description of the form r...
 14.6.13E: Parametric descriptions Give a parametric description of the form r...
 14.6.14E: Parametric descriptions Give a parametric description of the form r...
 14.6.15E: Parametric descriptions Give a parametric description of the form r...
 14.6.16E: Parametric descriptions Give a parametric description of the form r...
 14.6.23E: Surface area using a parametric description Find the area of the fo...
 14.6.25E: Surface area using a parametric description Find the area of the fo...
 14.6.26E: Surface area using a parametric description Find the area of the fo...
 14.6.27E: Surface integrals using a parametric description Evaluate the surfa...
 14.6.28E: Surface integrals using a parametric description Evaluate the surfa...
 14.6.29E: Surface integrals using a parametric description Evaluate the surfa...
 14.6.30E: Surface integrals using a parametric description Evaluate the surfa...
 14.6.31E: Surface area using an explicit description Find the area of the fol...
 14.6.32E: Surface area using an explicit description Find the area of the fol...
 14.6.33E: Surface area using an explicit description Find the area of the fol...
 14.6.34E: Surface area using an explicit description Find the area of the fol...
 14.6.20E: Identify the surface Describe the surface with the given parametric...
 14.6.35E: Surface integrals using an explicit description Evaluate the surfac...
 14.6.36E: Surface integrals using an explicit description Evaluate the surfac...
 14.6.18E: Identify the surface Describe the surface with the given parametric...
 14.6.37E: Surface integrals using an explicit description Evaluate the surfac...
 14.6.38E: Surface integrals using an explicit description Evaluate the surfac...
 14.6.39E: Average values Find the average temperature on that part of the pla...
 14.6.40E: Average values Find the average squared distance between the origin...
 14.6.44E: Surface integrals of vector fields Find the flux of the following v...
 14.6.45E: Surface integrals of vector fields Find the flux of the following v...
 14.6.46E: Surface integrals of vector fields Find the flux of the following v...
 14.6.47E: Surface integrals of vector fields Find the flux of the following v...
 14.6.48E: Surface integrals of vector fields Find the flux of the following v...
 14.6.49E: Explain why or why not Determine whether the following statements a...
 14.6.50E: Miscellaneous surface integrals Evaluate the following integrals us...
 14.6.51E: Miscellaneous surface integrals Evaluate the following integrals us...
 14.6.52E: Miscellaneous surface integrals Evaluate the following integrals us...
 14.6.53E: ·n dS, where S is the cylinder x2+ z2 = a2,
 14.6.54E: Cone and sphere The cone z2 = x2 + y2, for z ? 0, cuts the sphere x...
 14.6.55E: Cylinder and sphere Consider the sphere x2 + y2 + z2 = 4 and the cy...
 14.6.56E: Flux on a tetrahedron Find the upward flux of the fieldF = ? x, y, ...
 14.6.17E: Identify the surface Describe the surface with the given parametric...
 14.6.57E: Flux across a cone Consider the field F = ? x, y, z? and the cone z...
 14.6.58E: Surface area formula for cones Find the general formula for the sur...
 14.6.59E: Surface area formula for spherical cap A sphere of radius a is slic...
 14.6.60E: Radial fields and spheres Consider the radial field F = r/  r p. ...
Solutions for Chapter 14.6: Calculus: Early Transcendentals 1st Edition
Full solutions for Calculus: Early Transcendentals  1st Edition
ISBN: 9780321570567
Solutions for Chapter 14.6
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Chapter 14.6 includes 74 full stepbystep solutions. Since 74 problems in chapter 14.6 have been answered, more than 140660 students have viewed full stepbystep solutions from this chapter.

Absolute maximum
A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Circular functions
Trigonometric functions when applied to real numbers are circular functions

Conditional probability
The probability of an event A given that an event B has already occurred

Correlation coefficient
A measure of the strength of the linear relationship between two variables, pp. 146, 162.

Cosecant
The function y = csc x

Derivative of ƒ
The function defined by ƒ'(x) = limh:0ƒ(x + h)  ƒ(x)h for all of x where the limit exists

Identity matrix
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

Logarithm
An expression of the form logb x (see Logarithmic function)

Natural exponential function
The function ƒ1x2 = ex.

Natural numbers
The numbers 1, 2, 3, . . . ,.

Real part of a complex number
See Complex number.

Reduced row echelon form
A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.

Second
Angle measure equal to 1/60 of a minute.

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Supply curve
p = ƒ(x), where x represents production and p represents price

symmetric about the xaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Terms of a sequence
The range elements of a sequence.

Third quartile
See Quartile.

yintercept
A point that lies on both the graph and the yaxis.