 13.1.1: In Exercises 1 and 2, use the graph to determine whether is a funct...
 13.1.2: In Exercises 1 and 2, use the graph to determine whether is a funct...
 13.1.3: In Exercises 36, determine whether is a function of x and y
 13.1.4: In Exercises 36, determine whether is a function of x and y
 13.1.5: In Exercises 36, determine whether is a function of x and y
 13.1.6: In Exercises 36, determine whether is a function of x and y
 13.1.7: In Exercises 718, find and simplify the function values.
 13.1.8: In Exercises 718, find and simplify the function values.
 13.1.9: In Exercises 718, find and simplify the function values.
 13.1.10: In Exercises 718, find and simplify the function values.
 13.1.11: In Exercises 718, find and simplify the function values.
 13.1.12: In Exercises 718, find and simplify the function values.
 13.1.13: In Exercises 718, find and simplify the function values.fx, y x sin y
 13.1.14: In Exercises 718, find and simplify the function values.Vr, h r2h
 13.1.15: In Exercises 718, find and simplify the function values.gx, y yx2t ...
 13.1.16: In Exercises 718, find and simplify the function values.gx, y yx1tdt
 13.1.17: In Exercises 718, find and simplify the function values.x, y 2x y
 13.1.18: In Exercises 718, find and simplify the function values.fx, y 3x 2 2y
 13.1.19: In Exercises 1930, describe the domain and range of the function.fx...
 13.1.20: In Exercises 1930, describe the domain and range of the function.fx...
 13.1.21: In Exercises 1930, describe the domain and range of the function.gx...
 13.1.22: In Exercises 1930, describe the domain and range of the function.gx...
 13.1.23: In Exercises 1930, describe the domain and range of the function.z x y
 13.1.24: In Exercises 1930, describe the domain and range of the function.z ...
 13.1.25: In Exercises 1930, describe the domain and range of the function.fx...
 13.1.26: In Exercises 1930, describe the domain and range of the function.
 13.1.27: In Exercises 1930, describe the domain and range of the function.fx...
 13.1.28: In Exercises 1930, describe the domain and range of the function.fx...
 13.1.29: In Exercises 1930, describe the domain and range of the function.fx...
 13.1.30: In Exercises 1930, describe the domain and range of the function.fx...
 13.1.31: Think About It The graphs labeled (a), (b), (c), and (d) are graphs...
 13.1.32: Think About It Use the function given in Exercise 31. (a) Find the ...
 13.1.33: In Exercises 33 40, sketch the surface given by the function.fx, y 4
 13.1.34: In Exercises 33 40, sketch the surface given by the function.fx, y ...
 13.1.35: In Exercises 33 40, sketch the surface given by the function.fx, y ...
 13.1.36: In Exercises 33 40, sketch the surface given by the function.2 fx, ...
 13.1.37: In Exercises 33 40, sketch the surface given by the function.
 13.1.38: In Exercises 33 40, sketch the surface given by the function.
 13.1.39: In Exercises 33 40, sketch the surface given by the function.fx, y ex
 13.1.40: In Exercises 33 40, sketch the surface given by the function.fx, y ...
 13.1.41: In Exercises 4144, use a computer algebra system to graph the funct...
 13.1.42: In Exercises 4144, use a computer algebra system to graph the funct...
 13.1.43: In Exercises 4144, use a computer algebra system to graph the funct...
 13.1.44: In Exercises 4144, use a computer algebra system to graph the funct...
 13.1.45: In Exercises 4548, match the graph of the surface with one of the c...
 13.1.46: In Exercises 4548, match the graph of the surface with one of the c...
 13.1.47: In Exercises 4548, match the graph of the surface with one of the c...
 13.1.48: In Exercises 4548, match the graph of the surface with one of the c...
 13.1.49: In Exercises 4956, describe the level curves of the function. Sketc...
 13.1.50: In Exercises 4956, describe the level curves of the function. Sketc...
 13.1.51: In Exercises 4956, describe the level curves of the function. Sketc...
 13.1.52: In Exercises 4956, describe the level curves of the function. Sketc...
 13.1.53: In Exercises 4956, describe the level curves of the function. Sketc...
 13.1.54: In Exercises 4956, describe the level curves of the function. Sketc...
 13.1.55: In Exercises 4956, describe the level curves of the function. Sketc...
 13.1.56: In Exercises 4956, describe the level curves of the function. Sketc...
 13.1.57: In Exercises 5760, use a graphing utility to graph six level curves...
 13.1.58: In Exercises 5760, use a graphing utility to graph six level curves...
 13.1.59: In Exercises 5760, use a graphing utility to graph six level curves...
 13.1.60: In Exercises 5760, use a graphing utility to graph six level curves...
 13.1.61: What is a graph of a function of two variables? How is it interpret...
 13.1.62: All of the level curves of the surface given by are concentric circ...
 13.1.63: Construct a function whose level curves are lines passing through t...
 13.1.64: Consider the function for and (a) Sketch the graph of the surface g...
 13.1.65: Writing In Exercises 65 and 66, use the graphs of the level curves ...
 13.1.66: Writing In Exercises 65 and 66, use the graphs of the level curves ...
 13.1.67: Investment In 2009, an investment of $1000 was made in a bond earni...
 13.1.68: Investment A principal of $5000 is deposited in a savings account t...
 13.1.69: In Exercises 6974, sketch the graph of the level surface at the giv...
 13.1.70: In Exercises 6974, sketch the graph of the level surface at the giv...
 13.1.71: In Exercises 6974, sketch the graph of the level surface at the giv...
 13.1.72: In Exercises 6974, sketch the graph of the level surface at the giv...
 13.1.73: In Exercises 6974, sketch the graph of the level surface at the giv...
 13.1.74: In Exercises 6974, sketch the graph of the level surface at the giv...
 13.1.75: Forestry The Doyle Log Rule is one of several methods used to deter...
 13.1.76: Queuing Model The average length of time that a customer waits in l...
 13.1.77: Temperature Distribution The temperature (in degrees Celsius) at an...
 13.1.78: Electric Potential The electric potential at any point is Sketch th...
 13.1.79: CobbDouglas Production Function Use the CobbDouglas production fu...
 13.1.80: CobbDouglas Production Function Show that the CobbDouglas producti...
 13.1.81: Construction Cost A rectangular box with an open top has a length o...
 13.1.82: Volume A propane tank is constructed by welding hemispheres to the ...
 13.1.83: Ideal Gas Law According to the Ideal Gas Law, where is pressure, is...
 13.1.84: Modeling Data The table shows the net sales (in billions of dollars...
 13.1.85: Meteorology Meteorologists measure the atmospheric pressure in mill...
 13.1.86: Acid Rain The acidity of rainwater is measured in units called pH. ...
 13.1.87: Atmosphere The contour map shown in the figure was computer generat...
 13.1.88: Geology The contour map in the figure represents colorcoded seismic...
 13.1.89: True or False? In Exercises 8992, determine whether the statement i...
 13.1.90: True or False? In Exercises 8992, determine whether the statement i...
 13.1.91: True or False? In Exercises 8992, determine whether the statement i...
 13.1.92: True or False? In Exercises 8992, determine whether the statement i...
Solutions for Chapter 13.1: Introduction to Functions of Several Variables
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 13.1: Introduction to Functions of Several Variables
Get Full SolutionsCalculus was written by and is associated to the ISBN: 9780547167022. Chapter 13.1: Introduction to Functions of Several Variables includes 92 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus , edition: 9. This expansive textbook survival guide covers the following chapters and their solutions. Since 92 problems in chapter 13.1: Introduction to Functions of Several Variables have been answered, more than 61549 students have viewed full stepbystep solutions from this chapter.

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

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.

Census
An observational study that gathers data from an entire population

Control
The principle of experimental design that makes it possible to rule out other factors when making inferences about a particular explanatory variable

Cubic
A degree 3 polynomial function

Data
Facts collected for statistical purposes (singular form is datum)

Direction angle of a vector
The angle that the vector makes with the positive xaxis

Finite series
Sum of a finite number of terms.

Halfangle identity
Identity involving a trigonometric function of u/2.

Index
See Radical.

Initial value of a function
ƒ 0.

Integers
The numbers . . ., 3, 2, 1, 0,1,2,...2

Irrational numbers
Real numbers that are not rational, p. 2.

Nappe
See Right circular cone.

Position vector of the point (a, b)
The vector <a,b>.

Probability function
A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.

Quotient polynomial
See Division algorithm for polynomials.

Right angle
A 90° angle.

Sum of a finite arithmetic series
Sn = na a1 + a2 2 b = n 2 32a1 + 1n  12d4,

Sum of an infinite geometric series
Sn = a 1  r , r 6 1