 Chapter 1.1: The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations
 Chapter 1.2: Intercepts; Symmetry; Graphing Key Equations
 Chapter 1.3: Solving Equations Using a Graphing Utility
 Chapter 1.4: Lines
 Chapter 1.5: Circles
 Chapter 10.1: Conics
 Chapter 10.2: The Parabola
 Chapter 10.3: The Ellipse
 Chapter 10.4: The Hyperbola
 Chapter 10.5: Rotation of Axes; General Form of a Conic
 Chapter 10.6: Polar Equations of Conics
 Chapter 10.7: Plane Curves and Parametric Equations
 Chapter 11.1: Systems of Linear Equations: Substitution and Elimination
 Chapter 11.2: Systems of Linear Equations: Matrices
 Chapter 11.3: Systems of Linear Equations: Determinants
 Chapter 11.4: Matrix Algebra
 Chapter 11.5: Partial Fraction Decomposition
 Chapter 11.6: Systems of Nonlinear Equations
 Chapter 11.7: Systems of Inequalities
 Chapter 11.8: Linear Programming
 Chapter 12.1: Sequences
 Chapter 12.2: Arithmetic Sequences
 Chapter 12.3: Geometric Sequences; Geometric Series
 Chapter 12.4: Mathematical Induction
 Chapter 12.5: The Binomial Theorem
 Chapter 13.1: Sequences; Induction; the Binomial Theorem
 Chapter 13.2: Probability
 Chapter 14.1: Finding Limits Using Tables and Graphs
 Chapter 14.2: Algebra Techniques for Finding Limits
 Chapter 14.3: Onesided Limits; Continuous Functions
 Chapter 14.4: The Tangent Problem; The Derivative
 Chapter 14.5: The Area Problem; The Integral
 Chapter 2.1: Functions
 Chapter 2.2: The Graph of a Function
 Chapter 2.3: Properties of Functions
 Chapter 2.4: Library of Functions; Piecewisedefined Functions
 Chapter 2.5: Graphing Techniques: Transformations
 Chapter 2.6: Mathematical Models: Building Functions
 Chapter 3.1: Linear Functions and Their Properties
 Chapter 3.2: Linear Models: Building Linear Functions from Data
 Chapter 3.3: Quadratic Functions and Their Properties
 Chapter 3.4: Build Quadratic Models from Verbal Descriptions and from Data
 Chapter 3.5: Inequalities Involving Quadratic Functions
 Chapter 4.1: Polynomial Functions and Models
 Chapter 4.2: The Real Zeros of a Polynomial Function
 Chapter 4.3: Complex Zeros; Fundamental Theorem of Algebra
 Chapter 4.4: Properties of Rational Functions
 Chapter 4.5: The Graph of a Rational Function
 Chapter 4.6: Polynomial and Rational Inequalities
 Chapter 4.7: Polynomial and Rational Functions
 Chapter 5.1: Composite Functions
 Chapter 5.2: OnetoOne Functions; Inverse Functions
 Chapter 5.3: Exponential Functions
 Chapter 5.4: Logarithmic Functions
 Chapter 5.5: Properties of Logarithms
 Chapter 5.6: Logarithmic and Exponential Equations
 Chapter 5.7: Financial Models
 Chapter 5.70: Financial Models
 Chapter 5.8: Exponential Growth and Decay Models; Newtons Law; Logistic Growth and Decay Models
 Chapter 5.80: Exponential Growth and Decay Models; Newtons Law; Logistic Growth and Decay Models
 Chapter 5.9: Building Exponential, Logarithmic, and Logistic Models from Data
 Chapter 6.1: Angles and Their Measure
 Chapter 6.2: Trigonometric Functions: Unit Circle Approach
 Chapter 6.3: Properties of the Trigonometric Functions
 Chapter 6.4: Graphs of the Sine and Cosine Functions
 Chapter 6.5: Open the Period applet. On the screen you will see a slider. Move the point along the slider to see the role v plays in the graph of f1x2 = sin1vx2. Pay particular attention to the key points matched by color on each graph. For convenience the graph of g1
 Chapter 6.6: Phase Shift; Sinusoidal Curve Fitting 4
 Chapter 7.1: The Inverse Sine, Cosine, and Tangent Functions
 Chapter 7.2: The Inverse Trigonometric Functions (Continued)
 Chapter 7.3: Trigonometric Equations
 Chapter 7.4: Trigonometric Identities
 Chapter 7.5: Sum and Difference Formulas
 Chapter 7.6: Doubleangle and Halfangle Formulas
 Chapter 7.7: ProducttoSum and SumtoProduct Formulas
 Chapter 8.1: Right Triangle Trigonometry; Applications
 Chapter 8.2: The Law of Sines
 Chapter 8.3: The Law of Cosines
 Chapter 8.4: Area of a Triangle
 Chapter 8.5: Simple Harmonic Motion; Damped Motion; Combining Waves
 Chapter 9.1: Polar Coordinates
 Chapter 9.2: Polar Equations and Graphs
 Chapter 9.3: The Complex Plane; De Moivres Theorem
 Chapter 9.4: Vectors
 Chapter 9.5: The Dot Product
 Chapter 9.6: Vectors in Space
 Chapter 9.7: The Cross Product
 Chapter A.1: Algebra Essentials
 Chapter A.10: nth Roots; Rational Exponents
 Chapter A.2: Geometry Essentials
 Chapter A.3: Polynomials
 Chapter A.4: Synthetic Division
 Chapter A.5: Rational Expressions
 Chapter A.6: Solving Equations
 Chapter A.7: Complex Numbers; Quadratic Equations in the Complex Number System
 Chapter A.8: Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
 Chapter A.9: Interval Notation; Solving Inequalities
 Chapter Appendix B: The Limit of a Sequence; Infinite Series
 Chapter Chapter 1: Graphs
 Chapter Chapter 10: Analytic Geometry
 Chapter Chapter 11: Systems of Equations and Inequalities
 Chapter Chapter 12: Sequences; Induction; the Binomial Theorem
 Chapter Chapter 13: Sequences; Induction; the Binomial Theorem
 Chapter Chapter 14: Sequences; Induction; the Binomial Theorem
 Chapter Chapter 15: Sequences; Induction; the Binomial Theorem
 Chapter Chapter 16: Sequences; Induction; the Binomial Theorem
 Chapter Chapter 17: Sequences; Induction; the Binomial Theorem
 Chapter Chapter 2: Functions and Their Graphs
 Chapter Chapter 3: Linear and Quadratic Functions
 Chapter Chapter 4: Polynomial and Rational Functions
 Chapter Chapter 5: Exponential and Logarithmic Functions
 Chapter Chapter 6: Trigonometric Functions
 Chapter Chapter 7: Analytic Trigonometry
 Chapter Chapter 8: Applications of Trigonometric Functions
 Chapter Chapter 9: Polar Coordinates; Vectors
Precalculus Enhanced with Graphing Utilities 6th Edition  Solutions by Chapter
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Precalculus Enhanced with Graphing Utilities  6th Edition  Solutions by Chapter
Get Full SolutionsThis textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. The full stepbystep solution to problem in Precalculus Enhanced with Graphing Utilities were answered by Patricia, our top Math solution expert on 01/11/18, 01:38PM. Precalculus Enhanced with Graphing Utilities was written by Patricia and is associated to the ISBN: 9780132854351. Since problems from 114 chapters in Precalculus Enhanced with Graphing Utilities have been answered, more than 11544 students have viewed full stepbystep answer. This expansive textbook survival guide covers the following chapters: 114.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.
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