- 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
The numbers in Pascal’s triangle: nCr = anrb = n!r!1n - r2!
Characteristic polynomial of a square matrix A
det(xIn - A), where A is an n x n matrix
Combinations of n objects taken r at a time
There are nCr = n! r!1n - r2! such combinations,
Compounded k times per year
Interest compounded using the formula A = Pa1 + rkbkt where k = 1 is compounded annually, k = 4 is compounded quarterly k = 12 is compounded monthly, etc.
Extracting square roots
A method for solving equations in the form x 2 = k.
A graph of data in which consecutive data points are connected by line segments
Median (of a data set)
The middle number (or the mean of the two middle numbers) if the data are listed in order.
Angle measure equal to 1/60 of a degree.
nth power of a
The number with n factors of a , where n is the exponent and a is the base.
Permutations of n objects taken r at a time
There are nPr = n!1n - r2! such permutations
A procedure for fitting a quadratic function to a set of data.
Re-expression of data
A transformation of a data set.
Reflection across the x-axis
x, y and (x,-y) are reflections of each other across the x-axis.
A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.
Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system
Standard form of a polynomial function
ƒ(x) = an x n + an-1x n-1 + Á + a1x + a0
A matrix A = [aij] with the property aij = aji for all i and j
See Weighted mean.