Solutions for Chapter 1.2: Calculus: Early Transcendentals 1st Edition

A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

The set of points on the “edge” of a region

A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.

The central point in a circle, ellipse, hyperbola, or sphere

det(xIn - A), where A is an n x n matrix

A line segment with endpoints on the conic

An identity involving a trigonometric function of 2u

See Equilibrium point.

Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

Points that satisfy the constraints in a linear programming problem.

See Angle.

A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1 - z1) 1x - i z 22 Á 1x - z n where the z1 are the zeros of ƒ

A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

The number of degrees or radians in an angle

See Additive inverse of a real number and Additive inverse of a complex number.

The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.

Computer-generated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random

For an angle ? in standard position, a reference triangle is a triangle formed by the terminal side of angle ?, the x-axis, and a perpendicular dropped from a point on the terminal side to the x-axis. The angle in a reference triangle at the origin is the reference angle

To find one or more unknown sides or angles of a triangle