 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 10974 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 Patricia and is associated to the ISBN: 9780470888612.

Absolute value of a vector
See Magnitude of a vector.

Average velocity
The change in position divided by the change in time.

Component form of a vector
If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x, y, and zcomponents of the vector, respectively)

Doubleblind experiment
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment

Higherdegree polynomial function
A polynomial function whose degree is ? 3

Irreducible quadratic over the reals
A quadratic polynomial with real coefficients that cannot be factored using real coefficients.

LRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the lefthand endpoint of each subinterval

Multiplicative inverse of a real number
The reciprocal of b, or 1/b, b Z 0

Objective function
See Linear programming problem.

Order of magnitude (of n)
log n.

Random behavior
Behavior that is determined only by the laws of probability.

Rational zeros
Zeros of a function that are rational numbers.

Sequence of partial sums
The sequence {Sn} , where Sn is the nth partial sum of the series, that is, the sum of the first n terms of the series.

Speed
The magnitude of the velocity vector, given by distance/time.

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

Sum of complex numbers
(a + bi) + (c + di) = (a + c) + (b + d)i

Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)

System
A set of equations or inequalities.

Vertical stretch or shrink
See Stretch, Shrink.

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