Solutions for Chapter 12: Vector-Valued Functions

A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.

See Mathematical induction.

The numbers in Pascal’s triangle: nCr = anrb = n!r!1n - r2!

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

A polynomial that the function approaches as.

The area of ¢ABC with semiperimeter s is given by 2s1s - a21s - b21s - c2.

Using the science of statistics to make inferences about the parameters in a population from a sample.

An equation that can be written in the form ax + b = 0, where a and b are real numbers and a Z 0

An inequality that can be written in the form ax + b < 0 ,ax + b … 0 , ax + b > 0, or ax + b Ú 0, where a and b are real numbers and a Z 0

The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x - c) (x - z 2) Á (x - z n)

For any positive integer n, n factorial is n! = n.(n - 1) . (n - 2) .... .3.2.1; zero factorial is 0! = 1

A set of n objects.

A procedure for fitting a quadratic function to a set of data.

tan ?= sin ?cos ?and cot ?= cos ? sin ?

A procedure for finding the possible rational zeros of a polynomial.

If a polynomial f(x) is divided by x - c , the remainder is ƒ(c)

A logarithmic scale used in measuring the intensity of an earthquake.

A plot of all the ordered pairs of a two-variable data set on a coordinate plane.

An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

Vector of length 1.