I2 Subject Index in standard form, A59 sums of, A59 Complex number system, A58–A59 Complex plane, 627–636 plotting points in, 628 Complex polynomial functions, 230 Complex roots, 632–634 Complex variables, 230 Complex zeros of a polynomial function, 230–234 Conjugate Pairs Theorem and, 231–232 definition of, 230 finding, 233–234 given, finding functions with, 232–233 Components of a vector, 661 Composite functions, 273–280 in calculus, 277 components of, 277 definition of, 273 equal, 276–277 evaluating, 274 forming, 273–277 involving inverse trigonometric functions, exact value of, 489–490 Compound interest, 345–348 Compound interest formula, 346 Compound probabilities, 928–929 Compressions, graphing functions using, 115–117 Concave up/concave down parabolas, 159 Cones, right circular, 681 Congruent triangles, A16–A17 definition of, A16 Conics (conic sections), 681–735 circles, 48–55, 681 center of, 48 circumference of, A7 definition of, 48 equation of, standard form of, 48–49 graphing, 49–51 graphing polar equations and, 614–615 intercepts of, 50 radius of, 48 of radius r, to evaluate trigonometric functions, 406–407 tangent line to, 55 unit, 48–49 definition of, 729 degenerate, 681 eccentricity of, 729 ellipses, 681, 692–704 applied problems involving, 700 with center at h k , ( ), 697–699 with center at the origin, 693–697 definition of, 692, 729 equation of, 694, 695–697, 698, 699 graphs/graphing of, 695, 698–699 major axis of, 729 focus of, 729 general equation of, 726 hyperbolas, 681, 705–720 applied problems involving, 714–716 asymptotes of, 710–712 with center at h k , ( ), 712–714 with center at the origin, 705–710 conjugate, 719 definition of, 705, 729 equation of, 706–707, 708–710, 711–712, 713–714 equilateral, 719 graphs/graphing of, 706–707 transverse axis of, 729 identifying without completing the squares, 720–721 without rotating the axes, 726 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 definition of, 48 equations of general form of, 51–52 standard form of, 48–49 graphing, 49–51 graphing polar equations and, 614–615 intercepts of, 50 radius of, 48 of radius r, to evaluate trigonometric functions, 406–407 tangent line to, 55 unit, 48–49, 397–398 Circular functions, 398. See also Trigonometric functions Clark, William, 545, 598 Closed intervals, A77 Codomain of a function, 63 Coefficient(s) binomial, 901 correlation, 153 damping, 586 of friction, 649 leading, of a polynomial, 190, A22 of a monomial, A22 of a polynomial, 190, A22 Coefficient matrix, 771 Cofactors, 788 Cofunctions, 548 Column index of a matrix, 770, 795 Column vectors, product of a row vector and, 799 Combinations counting problems involving, 919–921 definition of, 920 listing, 920 Combinatorics, 911 Combined inequalities, solving, A81–A82 Common difference, 869 Common logarithm function, 318 Common ratio, 876 Commutative property of dot products, 652 of matrix addition, 797 of vector addition, 638 Complement(s) of an event, 930 of a set, A2, A3 Complementary angles, 548 Complementary Angle Theorem, 548 Complete graphs, 4–5 Completing the square, A29 identifying conics without, 720–721 solving quadratic equations using, A50–A51 Complex conjugates, A60–A62 Complex numbers, A58–A59 as complex roots, 632–634 conjugates of, A60–A62 converting between rectangular and polar or exponential form, 628–630 definition of, A59 De Moivre’s Theorem and, 631–632 difference of, A59 equality of, A59 historical feature on, 634 imaginary part of, A59 imaginary unit and, A58 magnitude or modulus of, 628 multiplying by conjugates, A60–A61 polar form of converting between rectangular form and, 628–631 definition of, 628 power of i and, A62–A63 products of, 630–631, A60 quotients of, 630–631 real part of, A59 reciprocal of, in standard form, A61 solving quadratic equations in the complex number system and, A63–A65 Bernoulli, Johan, 745 Bessel, Friedrich, 556 Best fit cubic model of, 210–211 line of, graphing utility to find, 152–153 Bézout, Étienne, 827 Binomial(s), A22 cubes of, formula for, A25 FOIL and, A24 squares of, formula for, A25 Binomial coefficient, 901 Binomial Theorem, 898–905 definition of, 899 evaluating n j ( ) using, 899–900 expanding a binomial using, 901 finding a coefficient in a binomial expansion and, 901–902 finding a term in a binomial expansion and, 902–903 historical feature on, 903 Bisection method, 228 Boole, George, 932 Bounded graphs, 837 Bounding curves, 587 Bounds on zeros of a polynomial function, 222–225 Brachistochrone, 745 Branches of a hyperbola, 705 Break-even point, 147 Briggs, Henry, 333 Bürgi, Joost, 333 Calculators approximating roots using, A88 arithmetic, A10 scientific, A10 values of a function on, 67 Calculus absolute maximum and absolute minimum in, 92 approximating f x ex ( ) = and, 813 composite functions in, 277 derivatives andin, 962–963 derivatives in, 68, 170, 246 difference quotient in, 68, 522 Double-angle Formulas and, 527, 526 functions and critical numbers for, 869 increasing, decreasing, or constant, 362 local maximum and local minimum in, 93 instantaneous rates of change and, 963–964 instantaneous velocity and, 964–966 integrals in, 972–974 limits in, 199, 237, 302, 879, 888, 941 partial fraction decomposition and, 813 polar equations and, 623 rational exponents and, A92 rationalizing the numerator in, A89n Snell’s Law and, 502 tangent problem and, 960 turning points in, 197 of variations, 745 vectors in, 637, 740 Carbon dating, 357 Cardano, Girolamo, 226, 634, 932 Cardioids, 616–617 Carrying capacity, 360 Cartesian coordinate system, 2 Cayley, Arthur, 808 Centers of a circle, 48 of an ellipse, 693 of a sphere, 668 Change-of-base formula, 332 Chebyshëv, P. L., 526n Chebyshëv polynomials, 526n Chu Shih-chieh, 903 Circles, 48–55, 681 center of, 48 circumference of, A7
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