 13.1.1: Determining Whether a Graph Is a Function In Exercises 1 and 2, use...
 13.1.2: Determining Whether a Graph Is a Function In Exercises 1 and 2, use...
 13.1.3: Determining Whether an Equation Is a Function In Exercises 36, dete...
 13.1.4: Determining Whether an Equation Is a Function In Exercises 36, dete...
 13.1.5: Determining Whether an Equation Is a Function In Exercises 36, dete...
 13.1.6: Determining Whether an Equation Is a Function In Exercises 36, dete...
 13.1.7: Evaluating a Function In Exercises 718, find and simplify the funct...
 13.1.8: Evaluating a Function In Exercises 718, find and simplify the funct...
 13.1.9: Evaluating a Function In Exercises 718, find and simplify the funct...
 13.1.10: Evaluating a Function In Exercises 718, find and simplify the funct...
 13.1.11: Evaluating a Function In Exercises 718, find and simplify the funct...
 13.1.12: Evaluating a Function In Exercises 718, find and simplify the funct...
 13.1.13: Evaluating a Function In Exercises 718, find and simplify the funct...
 13.1.14: Evaluating a Function In Exercises 718, find and simplify the funct...
 13.1.15: Evaluating a Function In Exercises 718, find and simplify the funct...
 13.1.16: Evaluating a Function In Exercises 718, find and simplify the funct...
 13.1.17: Evaluating a Function In Exercises 718, find and simplify the funct...
 13.1.18: Evaluating a Function In Exercises 718, find and simplify the funct...
 13.1.19: Finding the Domain and Range of a Function In Exercises 1930, find ...
 13.1.20: Finding the Domain and Range of a Function In Exercises 1930, find ...
 13.1.21: Finding the Domain and Range of a Function In Exercises 1930, find ...
 13.1.22: Finding the Domain and Range of a Function In Exercises 1930, find ...
 13.1.23: Finding the Domain and Range of a Function In Exercises 1930, find ...
 13.1.24: Finding the Domain and Range of a Function In Exercises 1930, find ...
 13.1.25: Finding the Domain and Range of a Function In Exercises 1930, find ...
 13.1.26: Finding the Domain and Range of a Function In Exercises 1930, find ...
 13.1.27: Finding the Domain and Range of a Function In Exercises 1930, find ...
 13.1.28: Finding the Domain and Range of a Function In Exercises 1930, find ...
 13.1.29: Finding the Domain and Range of a Function In Exercises 1930, find ...
 13.1.30: Finding the Domain and Range of a Function In Exercises 1930, find ...
 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: Sketching a Surface In Exercises 3340, sketch the surface given by ...
 13.1.34: Sketching a Surface In Exercises 3340, sketch the surface given by ...
 13.1.35: Sketching a Surface In Exercises 3340, sketch the surface given by ...
 13.1.36: Sketching a Surface In Exercises 3340, sketch the surface given by ...
 13.1.37: Sketching a Surface In Exercises 3340, sketch the surface given by ...
 13.1.38: Sketching a Surface In Exercises 3340, sketch the surface given by ...
 13.1.39: Sketching a Surface In Exercises 3340, sketch the surface given by ...
 13.1.40: Sketching a Surface In Exercises 3340, sketch the surface given by ...
 13.1.41: Graphing a Function Using Technology In Exercises 4144, use a compu...
 13.1.42: Graphing a Function Using Technology In Exercises 4144, use a compu...
 13.1.43: Graphing a Function Using Technology In Exercises 4144, use a compu...
 13.1.44: Graphing a Function Using Technology In Exercises 4144, use a compu...
 13.1.45: Matching In Exercises 4548, match the graph of the surface with one...
 13.1.46: Matching In Exercises 4548, match the graph of the surface with one...
 13.1.47: Matching In Exercises 4548, match the graph of the surface with one...
 13.1.48: Matching In Exercises 4548, match the graph of the surface with one...
 13.1.49: Sketching a Contour Map In Exercises 4956, describe the level curve...
 13.1.50: Sketching a Contour Map In Exercises 4956, describe the level curve...
 13.1.51: Sketching a Contour Map In Exercises 4956, describe the level curve...
 13.1.52: Sketching a Contour Map In Exercises 4956, describe the level curve...
 13.1.53: Sketching a Contour Map In Exercises 4956, describe the level curve...
 13.1.54: Sketching a Contour Map In Exercises 4956, describe the level curve...
 13.1.55: Sketching a Contour Map In Exercises 4956, describe the level curve...
 13.1.56: Sketching a Contour Map In Exercises 4956, describe the level curve...
 13.1.57: Graphing Level Curves In Exercises 5760, use a graphing utility to ...
 13.1.58: Graphing Level Curves In Exercises 5760, use a graphing utility to ...
 13.1.59: Graphing Level Curves In Exercises 5760, use a graphing utility to ...
 13.1.60: Graphing Level Curves In Exercises 5760, use a graphing utility to ...
 13.1.61: Function of Two Variables What is a graph of a function of two vari...
 13.1.62: Using Level Curves All of the level curves of the surface given by ...
 13.1.63: Creating a Function Construct a function whose level curves are lin...
 13.1.64: Conjecture Consider the function for and (a) Sketch the graph of th...
 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 2012, 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: Sketching a Level Surface In Exercises 6974, sketch the graph of th...
 13.1.70: Sketching a Level Surface In Exercises 6974, sketch the graph of th...
 13.1.71: Sketching a Level Surface In Exercises 6974, sketch the graph of th...
 13.1.72: Sketching a Level Surface In Exercises 6974, sketch the graph of th...
 13.1.73: Sketching a Level Surface In Exercises 6974, sketch the graph of th...
 13.1.74: Sketching a Level Surface In Exercises 6974, sketch the graph of th...
 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 Cobb Douglas production f...
 13.1.80: CobbDouglas Production Function Show that the CobbDouglas product...
 13.1.81: Ideal Gas Law According to the Ideal Gas Law, where is pressure, is...
 13.1.82: Modeling Data The table shows the net sales (in billions of dollars...
 13.1.83: Meteorology Meteorologists measure the atmospheric pressure in mill...
 13.1.84: Acid Rain The acidity of rainwater is measured in units called pH. ...
 13.1.85: Construction Cost A rectangular box with an open top has a length o...
 13.1.86: HOW DO YOU SEE IT? The contour map shown in the figure was computer...
 13.1.87: True or False? In Exercises 8790, determine whether the statement i...
 13.1.88: True or False? In Exercises 8790, determine whether the statement i...
 13.1.89: True or False? In Exercises 8790, determine whether the statement i...
 13.1.90: True or False? In Exercises 8790, determine whether the statement i...
 13.1.91: True or False? In Exercises 8790, determine whether the statement i...
Solutions for Chapter 13.1: Introduction to Functions of Several Variables
Full solutions for Calculus: Early Transcendental Functions  6th Edition
ISBN: 9781285774770
Solutions for Chapter 13.1: Introduction to Functions of Several Variables
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions, edition: 6. Chapter 13.1: Introduction to Functions of Several Variables includes 91 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9781285774770. Since 91 problems in chapter 13.1: Introduction to Functions of Several Variables have been answered, more than 43703 students have viewed full stepbystep solutions from this chapter.

Absolute value of a real number
Denoted by a, represents the number a or the positive number a if a < 0.

Angle of elevation
The acute angle formed by the line of sight (upward) and the horizontal

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

Causation
A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable

Center
The central point in a circle, ellipse, hyperbola, or sphere

Dependent variable
Variable representing the range value of a function (usually y)

Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x)  ƒ(a) x  a provided the limit exists

Geometric sequence
A sequence {an}in which an = an1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

Halflife
The amount of time required for half of a radioactive substance to decay.

Imaginary part of a complex number
See Complex number.

Inverse of a matrix
The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

Matrix, m x n
A rectangular array of m rows and n columns of real numbers

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

nth root of a complex number z
A complex number v such that vn = z

Opposite
See Additive inverse of a real number and Additive inverse of a complex number.

Present value of an annuity T
he net amount of your money put into an annuity.

Rectangular coordinate system
See Cartesian coordinate system.

Right angle
A 90° angle.

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.

Transitive property
If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.