 13.R.1E: What is a realvalued function of two independent variables? Three ...
 13.R.2E: What does it mean for sets in the plane or in space to be open? Clo...
 13.R.3E: How can you display the values of a function ƒ(x, y) of two indepen...
 13.R.4E: What does it mean for a function ƒ(x, y) to have limit L as What ar...
 13.R.5E: When is a function of two (three) independent variables continuous ...
 13.R.6E: What can be said about algebraic combinations and composites of con...
 13.R.7E: Explain the twopath test for nonexistence of limits.
 13.R.8E: How are the partial derivatives of a function ƒ(x, y) defined? How ...
 13.R.9E: How does the relation between first partial derivatives and continu...
 13.R.11E: What does it mean for a function ƒ(x, y) to be differentiable? What...
 13.R.10E: What is the Mixed Derivative Theorem for mixed secondorder partial...
 13.R.12E: How can you sometimes decide from examining fx and fy that a functi...
 13.R.13E: What is the general Chain Rule? What form does it take for function...
 13.R.14E: What is the derivative of a function ƒ(x, y) at a point p0 in the d...
 13.R.15E: What is the gradient vector of a differentiable function ƒ(x, y)? H...
 13.R.16E: How do you find the tangent line at a point on a level curve of a d...
 13.R.17E: How can you use directional derivatives to estimate change?
 13.R.18E: How do you linearize a function ƒ(x, y) of two independent variable...
 13.R.19E: What can you say about the accuracy of linear approximations of fun...
 13.R.20E: If (x, y) moves from (x0,y0) to a point nearby , how can you estima...
 13.R.21E: How do you define local maxima, local minima, and saddle points for...
 13.R.22E: What derivative tests are available for determining the local extre...
 13.R.23E: How do you find the extrema of a continuous function ƒ(x, y) on a c...
 13.R.24E: Describe the method of Lagrange multipliers and give examples.
Solutions for Chapter 13.R: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321717399
Solutions for Chapter 13.R
Get Full SolutionsChapter 13.R includes 24 full stepbystep solutions. This textbook survival guide was created for the textbook: University Calculus: Early Transcendentals , edition: 2. University Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321717399. This expansive textbook survival guide covers the following chapters and their solutions. Since 24 problems in chapter 13.R have been answered, more than 62175 students have viewed full stepbystep solutions from this chapter.

Binomial theorem
A theorem that gives an expansion formula for (a + b)n

Complex number
An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers

Course
See Bearing.

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

Finite series
Sum of a finite number of terms.

First octant
The points (x, y, z) in space with x > 0 y > 0, and z > 0.

Hyperboloid of revolution
A surface generated by rotating a hyperbola about its transverse axis, p. 607.

Index of summation
See Summation notation.

Inequality
A statement that compares two quantities using an inequality symbol

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

Magnitude of a vector
The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2

Midpoint (on a number line)
For the line segment with endpoints a and b, a + b2

Nappe
See Right circular cone.

PH
The measure of acidity

Reciprocal of a real number
See Multiplicative inverse of a real number.

Removable discontinuity at x = a
lim x:a ƒ(x) = limx:a+ ƒ(x) but either the common limit is not equal ƒ(a) to ƒ(a) or is not defined

Secant
The function y = sec x.

Stretch of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal stretch) by the constant 1/c, or all of the ycoordinates (vertical stretch) of the points by a constant c, c, > 1.

Symmetric matrix
A matrix A = [aij] with the property aij = aji for all i and j