Solutions for Chapter 8: Techniques of Integration

The case in which two sides and a nonincluded angle can determine two different triangles

A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

ƒ'(a) = lim x:a ƒ(x) - ƒ(a) x - a provided the limit exists

The gathering and processing of numerical information

Arrows that have the same magnitude and direction.

The points (x, y, z) in space with x > 0 y > 0, and z > 0.

See Mathematical induction.

See Power function.

A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.

The diagonal from the top left to the bottom right of a square matrix

For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)

A square matrix with nonzero determinant

An annuity in which deposits are made at the same time interest is posted.

In an experimental study, an inactive treatment that is equivalent to the active treatment in every respect except for the factor about which an inference is to be made. Subjects in a blind experiment do not know if they have been given the active treatment or the placebo.

See Polar coordinate system.

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

In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.

See Right circular cone.