Solutions for Chapter 12: Vector-Valued Functions

P(A or B) = P(A) + P(B) - P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

0 + 0i is the complex number zero

A sample that sacrifices randomness for convenience

The function y = csc x

The factor Ae-a in an equation such as y = Ae-at cos bt

The function defined by ƒ'(x) = limh:0ƒ(x + h) - ƒ(x)h for all of x where the limit exists

Matrices that have the same order and equal corresponding elements.

A variable that affects a response variable.

The directed distance from the vertex to the focus.

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

The composition of a one-toone function with its inverse results in the identity function.

The function y = cot-1 x

The number of degrees or radians in an angle

If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(A|B) # P(B)

See Trigonometric form of a complex number.

See Radical.

The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).

A graph of a polar equation or r = a cos nu.

Ratio change in y/change in x

The directed distance from the x-axis xz-plane to a point in a plane (space), or the second number in an ordered pair (triple), pp. 12, 629.