Solutions for Chapter 3.1: Calculus: Early Transcendentals 1st Edition

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

a + (b + c) = (a + b) + c, a(bc) = (ab)c.

The function ƒ(x) = 1 / 1 + e-x

A function is bounded below if there is a number b such that b ? ƒ(x) for all x in the domain of f.

If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x-, y-, and z-components of the vector, respectively)

The directed distance from the vertex to the focus.

Graphing calculator or a computer with graphing software.

See Complex number.

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.

Arc of a circle between the initial side and terminal side of a central 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 path along which an object travels

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

A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

A distribution of data shaped like the normal curve.

A complex number v such that vn = 1

See Parametric equations.

An equation that can be written in the form ax 2 + bx + c = 01a ? 02

A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

(a + bi) + (c + di) = (a + c) + (b + d)i