Subject Index I9 Peano, Giuseppe, 932 Perfect cubes, formula for, A25 Perfect roots, A87 Perfect squares, formula for, A25 Perihelion, 703, 734, 753 Period(s) of an object in simple harmonic motion, 584 of a sinusoidal function, 431–432, 452–454 of a trigonometric function, 415–416 Periodic functions, 415 Periodic properties, 415 Permutations computing, 919 counting problems involving n distinct objects and, 917–919 counting problems involving n nondistinct objects and, 922 definition of, 917 Perpendicular lines, 42–43 Phase shift of a sinusoidal function, 452–454 Piecewise-defined functions, 105–107 continuous at a number, determining, 957 Pixels, 3 Plane curves defined by rectangular equations, parametric equations for, 743–745 defined parametrically, rectangular equation for, 738–740 definition of, 736 graphs/graphing of, 736 Plotting points, 2 in complex plane, 627–628 graphing equations by, 4–6 using polar coordinates, 600–602 Point(s) distance between, A6 distance from origin to, 126–127 finding distance between, 13–14 finding slope of a line given two points and, 34 finding the equation of a line given two points, 39 graphing a line given slope and, 35 plotting, 2 in complex plane, 627–628 graphing equations by, 4–6 using polar coordinates, 600–602 Point of tangency, 55 Point-slope form of a line, 36–37 Polar axis, 600 Polar coordinates, 600–610 converting from rectangular coordinates to, 604–606 converting to rectangular coordinates from, 602–604 historical feature on, 624 plotting points using, 600–602 transforming equations between polar and rectangular forms and, 606–607 Polar equations, 610–627 classification of, 622–623 definition of, 610 graphs/graphing of, 611–612 cardioids and, 616–617 by converting to rectangular equations, 611–612 with a graphing utility, 612–615 lemniscates and, 621 limaçons with an inner loop and, 619 limaçons without an inner loop and, 618 by plotting points, 616–624 roses and, 620 sketching quickly and, 623 spirals and, 621–622 identifying, 611–612 testing for symmetry, 615–616 Polar form of complex numbers, 628–631 complex roots and, 633 converting complex numbers between rectangular form and, 628–631 definition of, 628 Polar grids, 610 Pole, 600 Objective function, 841 Oblique asymptotes, rational functions and, 239, 241–244 Oblique triangles, 559–560 Odd-even properties, finding exact values of trigonometric functions using, 422–423 Odd functions definition of, 87 identifying, 87–89 One-sided limits, 953–955 One-to-one functions, 281–283 definition of, 281 graph of, obtaining inverse function from, 285 horizontal-line test for, 282–283 Open intervals, A77 Optimization, 171 Ordered pairs, 2 inverse functions defined by, 283–284 relations expressed using sets of, 61, 64 Ordinate, 2 Orientation along a plane curve, 736 Origin, 2, 660 distance to a point on a graph, 126–127 of real number line, A4 testing equations for symmetry with respect to, 22, 23 Orthogonal vectors, 654 decomposing a vector into, 654–656 finding, 672 Outcomes, 926 equally likely, 928–929 Output of a relation, 61 Parabolas, 158, 681, 682–692. See also Quadratic functions applied problems involving, 688–689 axis of symmetry of, 159, 160, 161–163, 682 concave up and concave down, 159 definition of, 682, 729 equation of, 683, 684–687 graphs/graphing, 683 with vertex at h k ( ), 686–687 with vertex at the origin, 682–686 vertex of, 159, 160–163 Paraboloid of revolution, 688–689 Parallelepipeds, 674 Parallel lines, equations of, 40–41 Parallelogram, area of, finding, 672–673 Parallel vectors, 653–654 Parameters, 736 Parametric equations for a cycloid, 744–745 definition of, 736 graphs/graphing of with graphing utility, 737–738 by hand, 736 for plane curves defined by rectangular equations, 743–745 rectangular equation for a plane curve defined parametrically and, 738–740 time as a parameter in, 740–742 Partial fraction(s), 813 Partial fraction decomposition, 812–820 identifying proper and improper rational expressions and, 813–814 where denominator has a nonrepeated irreducible quadratic factor, 817–818 where denominator has a repeated irreducible quadratic factor, 818–819 where denominator has only nonrepeated linear factors, 814–815 where denominator has repeated linear factors, 815–817 Partial sums, sequences of, 891 Participation rate, 76 Pascal, Blaise, 745, 931 Pascal triangle, 900, 904 Payment period, 345 Monomials coefficient of, A22 definition of, A22 degree of, A22 examples of, A22 limits of, 948–949 recognizing, A22–A23 Motion curvilinear, 740 damped, analyzing an object in, 586–588 harmonic, simple analyzing, 585–586 model for an object in, 583–585 parametric equations for an object in motion and, 743–744 projectile, 740–741 uniform motion formula and, A70 uniform motion problems and, A70–A71 Multiplication. See also Product(s) of a complex number by its conjugate, A60–A61 of matrices, 800–803 definition of, 800 of rational expressions, A36–A37 of vectors, geometric, 638–639 Multiplication principle of counting, 913–914 Multiplication property of inequalities, A79 Multiplicity rational functions and, vertical asymptotes and, 240–241 of real zeros (roots) of polynomial functions, 196–197 solving polynomial inequalities and, 260–261 Multiplier, 885 Mutually exclusive events, 930 Napier, John, 333 Nappes of a right circular cone, 681 Natural logarithm(s), 333 Natural logarithm function, 316 Natural numbers, A3 Negative real numbers, A4 Newton, Isaac, 359n Newton’s Law of Cooling, 359–360 Newton’s Method, 246 Niccolo of Brescia, 226 Nonlinear equations, systems of, 821–831 elimination method to solve, 822–826 historical feature on, 827 substitution method to solve, 821–822 Nonlinear functions, 139 Nonlinear relations, linear relations vs., 150–152 Nonnegative property of inequalities, A78 Nonstrict inequalities, A5 Normal line, 820 Notation function, 65 interval, A77–A78 summation, 859–860 properties of, 861 nth roots, A87–A88 principal, definition of, A87 nth term of an infinite series, 890 Null set, A1 Number(s) complex. See Complex numbers counting (natural), A3 Euler’s, 302 Fibonacci, 859–860 imaginary, pure, A59 irrational, A3, A58 rational, A3, A58 real, A3–A4 as coordinates of P, A4 positive and negative, A4 as scalars, 638–639 triangular, 868 Number e, 302 Numerators, A36 rationalizing, A89–A90, A89n
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