 12.5.1: Match the following functions with the level surfaces inFigure 12.8...
 12.5.2: Match the functions with the level surfaces in Figure12.82.(a) f(x,...
 12.5.3: Write the level surface x + 2y + 3z = 5 as the graph ofa function f...
 12.5.4: Find a formula for a function f(x, y, z) whose level surfacef = 4 i...
 12.5.5: Write the level surface x2 + y + z = 1 as the graph ofa function f(...
 12.5.6: Find a formula for a function f(x, y, z) whose level surfacesare sp...
 12.5.7: Which of the graphs in the catalog of surfaces onpage 702 is the gr...
 12.5.8: Use the catalog on page 702 to identify the surfaces in Exercises81...
 12.5.9: Use the catalog on page 702 to identify the surfaces in Exercises81...
 12.5.10: Use the catalog on page 702 to identify the surfaces in Exercises81...
 12.5.11: Use the catalog on page 702 to identify the surfaces in Exercises81...
 12.5.12: In Exercises 1215, decide if the given level surface can beexpresse...
 12.5.13: In Exercises 1215, decide if the given level surface can beexpresse...
 12.5.14: In Exercises 1215, decide if the given level surface can beexpresse...
 12.5.15: In Exercises 1215, decide if the given level surface can beexpresse...
 12.5.16: In 1618, represent the surface whose equation isgiven as the graph ...
 12.5.17: In 1618, represent the surface whose equation isgiven as the graph ...
 12.5.18: In 1618, represent the surface whose equation isgiven as the graph ...
 12.5.19: Suppose the function f(x, y, z)=2x 3y + z 20gives the temperature, ...
 12.5.20: The balance, B, in dollars, in a bank account dependson the amount ...
 12.5.21: The monthly payments, P dollars, on a mortgage inwhich A dollars we...
 12.5.22: Find a function f(x, y, z) whose level surface f = 1 isthe graph of...
 12.5.23: Find two functions f(x, y) and g(x, y) so that the graphsof both to...
 12.5.24: Find a formula for a function g(x, y, z) whose level surfacesare pl...
 12.5.25: The surface S is the graph of f(x, y) = 1 x2 y2.(a) Explain why S i...
 12.5.26: The surface S is the graph of f(x, y) = 1 y2.(a) Explain why S is t...
 12.5.27: A cone C, with height 1 and radius 1, has its base inthe xzplane a...
 12.5.28: Describe the level surface f(x, y, z) = x2/4 + z2 = 1in words.
 12.5.29: Describe the level surface g(x, y, z) = x2+y2/4+z2 =1 in words. [Hi...
 12.5.30: Describe in words the level surfaces of the functiong(x, y, z) = x ...
 12.5.31: Describe in words the level surfaces of f(x, y, z) =sin(x + y + z).
 12.5.32: Describe the surface x2 + y2 = (2 + sin z)2. In general,if f(z) 0 f...
 12.5.33: What do the level surfaces of f(x, y, z) = x2 y2 + z2look like? [Hi...
 12.5.34: Describe in words the level surfaces of g(x, y, z) =e(x2+y2+z2).
 12.5.35: Sketch and label level surfaces of h(x, y, z) = ezy forh = 1, e, e2.
 12.5.36: Sketch and label level surfaces of f(x, y, z)=4 x2 y2 z2 for f = 0,...
 12.5.37: Sketch and label level surfaces of g(x, y, z)=1 x2 y2 for g = 0, 1, 2.
 12.5.38: In 3840, explain what is wrong with the statement.The graph of a fu...
 12.5.39: In 3840, explain what is wrong with the statement.The level surface...
 12.5.40: In 3840, explain what is wrong with the statement.The level surface...
 12.5.41: In 4144, give an example of:A function f(x, y, z) whose level surfa...
 12.5.42: In 4144, give an example of:A function f(x, y, z) whose level sets ...
 12.5.43: In 4144, give an example of:A nonlinear function f(x, y, z) whose l...
 12.5.44: In 4144, give an example of:A function f(x, y, z) whose level sets ...
 12.5.45: Are the statements in 4554 true or false? Give reasonsfor your answ...
 12.5.46: Are the statements in 4554 true or false? Give reasonsfor your answ...
 12.5.47: Are the statements in 4554 true or false? Give reasonsfor your answ...
 12.5.48: Are the statements in 4554 true or false? Give reasonsfor your answ...
 12.5.49: Are the statements in 4554 true or false? Give reasonsfor your answ...
 12.5.50: Are the statements in 4554 true or false? Give reasonsfor your answ...
 12.5.51: Are the statements in 4554 true or false? Give reasonsfor your answ...
 12.5.52: Are the statements in 4554 true or false? Give reasonsfor your answ...
 12.5.53: Are the statements in 4554 true or false? Give reasonsfor your answ...
 12.5.54: Are the statements in 4554 true or false? Give reasonsfor your answ...
Solutions for Chapter 12.5: FUNCTIONS OF THREE VARIABLES
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 12.5: FUNCTIONS OF THREE VARIABLES
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Since 54 problems in chapter 12.5: FUNCTIONS OF THREE VARIABLES have been answered, more than 23457 students have viewed full stepbystep solutions from this chapter. Chapter 12.5: FUNCTIONS OF THREE VARIABLES includes 54 full stepbystep solutions. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612.

Algebraic expression
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

Aphelion
The farthest point from the Sun in a planet’s orbit

Cosine
The function y = cos x

Domain of a function
The set of all input values for a function

Feasible points
Points that satisfy the constraints in a linear programming problem.

Fibonacci numbers
The terms of the Fibonacci sequence.

Frequency distribution
See Frequency table.

General form (of a line)
Ax + By + C = 0, where A and B are not both zero.

Inverse cosine function
The function y = cos1 x

Inverse relation (of the relation R)
A relation that consists of all ordered pairs b, a for which a, b belongs to R.

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

Partial fractions
The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.

Pascal’s triangle
A number pattern in which row n (beginning with n = 02) consists of the coefficients of the expanded form of (a+b)n.

Quotient identities
tan ?= sin ?cos ?and cot ?= cos ? sin ?

Remainder polynomial
See Division algorithm for polynomials.

Remainder theorem
If a polynomial f(x) is divided by x  c , the remainder is ƒ(c)

Response variable
A variable that is affected by an explanatory variable.

Sphere
A set of points in Cartesian space equally distant from a fixed point called the center.

Xscl
The scale of the tick marks on the xaxis in a viewing window.

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