Solutions for Chapter 12: Vector-Valued Functions

An angle whose vertex is the center of a circle

The probability of an event A given that an event B has already occurred

A statement that describes a bounded interval, such as 3 ? x < 5

A sequence in which the kth term is given as a function of k.

A series whose terms form a geometric sequence.

A function ƒ is increasing on an interval I if, for any two points in I, a positive change in x results in a positive change in.

See Angle.

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

The value of |r| at the point on the graph of a polar equation that has the maximum distance from the pole

The perpendicular bisector of the major axis of an ellipse with endpoints on the ellipse.

The reciprocal of a + bi, or 1 a + bi = a a2 + b2- ba2 + b2 i

NDER f(a) = ƒ1a + 0.0012 - ƒ1a - 0.00120.002

A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

A relationship between two variables in which higher values of one variable are generally associated with higher values of the other variable, p. 717.

An expression that can be written as a ratio of two polynomials.

See Cartesian coordinate system.

A solution.

The magnitude of the velocity vector, given by distance/time.

If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.

The points x, 0, z in Cartesian space.