- 13.R.1E: What is a real-valued 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 two-path 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 second-order 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
A theorem that gives an expansion formula for (a + b)n
An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers
The number found when the corresponding components of two vectors are multiplied and then summed
A function whose domain is the first n positive integers for some fixed integer n.
Sum of a finite number of terms.
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.
A statement that compares two quantities using an inequality symbol
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the left-hand 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
See Right circular cone.
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
The function y = sec x.
Stretch of factor c
A transformation of a graph obtained by multiplying all the x-coordinates (horizontal stretch) by the constant 1/c, or all of the y-coordinates (vertical stretch) of the points by a constant c, c, > 1.
A matrix A = [aij] with the property aij = aji for all i and j