- 13.1: What is a real-valued function of two independent variables? Three ...
- 13.2: What does it mean for sets in the plane or in space to be open?Clos...
- 13.3: How can you display the values of a function (x, y) of two inde-pen...
- 13.4: What does it mean for a function (x, y) to have limit L as (x, y)S(...
- 13.5: When is a function of two (three) independent variables continu-ous...
- 13.6: What can be said about algebraic combinations and composites of con...
- 13.7: Explain the two-path test for nonexistence of limits.
- 13.8: How are the partial derivatives 0>0x and 0>0y of a function (x, y) ...
- 13.9: How does the relation between first partial derivatives and conti-n...
- 13.10: What is the Mixed Derivative Theorem for mixed second-order partial...
- 13.11: What does it mean for a function (x, y) to be differentiable? What ...
- 13.12: How can you sometimes decide from examining x and y that a function...
- 13.13: What is the general Chain Rule? What form does it take for func-tio...
- 13.14: What is the derivative of a function (x, y) at a point P0 in the di...
- 13.15: What is the gradient vector of a differentiable function (x, y)? Ho...
- 13.16: How do you find the tangent line at a point on a level curve of a d...
- 13.17: How can you use directional derivatives to estimate change?
- 13.18: How do you linearize a function (x, y) of two independent vari-able...
- 13.19: What can you say about the accuracy of linear approximations of fun...
- 13.20: If (x, y) moves from (x0, y0) to a point (x0+dx, y0+dy) nearby, how...
- 13.21: How do you define local maxima, local minima, and saddle points for...
- 13.22: What derivative tests are available for determining the local extre...
- 13.23: How do you find the extrema of a continuous function (x, y) on a cl...
- 13.24: Describe the method of Lagrange multipliers and give examples.
Solutions for Chapter 13: University Calculus: Early Transcendentals 3rd Edition
Full solutions for University Calculus: Early Transcendentals | 3rd Edition
See Inverse cosine function.
Average rate of change of ƒ over [a, b]
The number ƒ(b) - ƒ(a) b - a, provided a ? b.
Complements or complementary angles
Two angles of positive measure whose sum is 90°
Initial side of an angle
Inverse secant function
The function y = sec-1 x
Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.
Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x:- q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large
Line of symmetry
A line over which a graph is the mirror image of itself
Magnitude of an arrow
The magnitude of PQ is the distance between P and Q
Two lines that are both vertical or have equal slopes.
An arrangement of elements of a set, in which order is important.
Projection of u onto v
The vector projv u = au # vƒvƒb2v
A statistical measure that does not change much in response to outliers.
A plot of all the ordered pairs of a two-variable data set on a coordinate plane.
Solution set of an inequality
The set of all solutions of an inequality
p = ƒ(x), where x represents production and p represents price
Symmetric difference quotient of ƒ at a
ƒ(x + h) - ƒ(x - h) 2h
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.
A shift of a graph up or down.
The y-value of the bottom of the viewing window.