Subject Index I7 finding, 482 properties of, exact values of composite functions and, 479–481 secant definition of, 487 exact value of, 487–489 sine definition of, 472–473 exact value of, 474–475 solving equations involving, 482–483 tangent definition of, 477–478 exact value of, 478–479 Irrational numbers, A3, A58 Irreducible quadratic factors, 222 Jefferson, Thomas, 545 Johnson, Katherine, 62 Johnson, Lonnie, 4 Karmarkar, Narendra, 840n Khayyám, Omar, 903 Kirchhoff’s Rules, 768, 782–783 Law of Cosines, 570–577 applied problems using, 572–573 historical feature on, 573 solving SAS triangles using, 571 solving SSS triangles using, 571–572 Law of Demand, 171 Law of Sines, 560–565 applied problems using, 563–565 historical feature on, 573 proof of, 565 solving SAA or ASA triangles using, 560–561 solving SSA triangles using, 561–563 Law of Tangents, historical feature on, 573 Law of uninhibited decay, 357–358 Law of uninhibited growth, 355–357 Laws of Exponents, 295, A7–A9 Leading coefficient of a polynomial, 190, A22 Leading terms of a polynomial, A22 of a polynomial function, 190 Least common multiple (LCM) method, A39–A40 Left endpoint, A77 Left-hand limit, 954 Lemniscates, 28, 621 Length of a line segment, 15 Lewis, Meriwether, 545, 598 Library of functions, 100–105 Lift, 599 Like radicals, combining, A88 Like terms, A22 Limaçons, 28 with an inner loop, 619 without an inner loop, 618 Limits, 198, 941–946 algebraic techniques for finding, 946–953 of an average rate of change, 951 calculus and, 941 of a constant, 946 of a difference, 947–948 graphs for investigating, 943–944 idea of, 941 of the identity function, 946 infinite, 198 at infinity, 198 of a monomial, 948–949 one-sided, 953–955 of a polynomial, 949 of a power or root, 949–950 of a product, 948 of a quotient, 950–951 of a sequence, 887–889 of a sum, 947 tables for investigating, 941–943 nonstrict, A5 in one variable, A80–A81 polynomial, solving graphically and algebraically, 259–261 multiplicity and, 260–261 properties of, A78–A78 sides of, A5 solutions of, A80 solving, A80–A81 strict, A5 in two variables, 834–840 graphing by hand, 831–833 graphing using a graphing utility, 833–834 satisfying, 831 systems of, graphing, 834–837 Inequality symbols, A4 Infinite geometric series, 879 Infinite limits, 198 Infinite series, 889–891 definition of, 890 sum of, 891 terms of, 890 Infinite sets, 911n Infinity, limits at, 198 Initial point of a geometric vector, 637 Initial value of a function, 143 Input of a relation, 61 Instantaneous rates of change, 963–964 Instantaneous velocity, 964–966 Integrals, approximating using a graphing utility, 972–974 Intercepts approximating using a graphing utility, 9–10 of a circle, 50 finding algebraically from an equation, 20–21, 23 finding from a graph, 9 graphing an equation in general form using, 39–40 Interest, A67 compound, 345–348 simple, 345, A67–A68 Interest problems, A67–A68 Interest rate, 345, A67 effective, 349 required to double a lump sum, 350–351 Intermediate Value Theorem, 225 Intersection of sets, A2, A3 Interval(s), A77 Interval notation, A77–A78 Invariance, 728 Inverse functions, 283–289 defined by a mapping or a set of ordered pairs, 283–284 definition of, 283 of a domain-restricted function, 289 of a function defined by an equation, 286–289 graph of, obtaining from graph of a one-to-one function, 285 of a logarithmic function, 316–319 trigonometric. See Inverse trigonometric functions verifying, 286–287 Inverse matrices, 803–807 definition of, 803 finding, 805–806 lack of, showing, 806 multiplying a matrix by, 804–805 solving a system of linear equations using, 807 solving systems of linear equations using, 807 Inverse trigonometric equations, solving, 482–483 Inverse trigonometric functions approximating value of, 488–489 composite functions involving, exact value of, 489–490 cosecant definition of, 487 exact value of, 487–489 cosine definition of, 475–476 exact value of, 476–477 cotangent definition of, 487 exact value of, 487–489 Harmonic motion, simple analyzing, 585–586 model for an object in, 583–585 Heron of Alexandria, 579 Heron’s Formula, historical feature on, 579 Hopper, Grace, 472 Horizontal asymptotes definition of, 239 rational functions and, 239, 241–244 Horizontal components of vectors, 641 Horizontal compressions and stretches, graphing functions using, 116 Horizontal lines equation of, 37 graphing polar equations and, 612, 614 Horizontal-line test, 282–283 Horizontal shifts, graphing functions using, 112–114 Hunt, Fern, 600 Huygens, Christiaan, 745, 931 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 Hyperboloids, 718 Hypocycloid, 748 Hypotenuse, 546, A14 Identities, A44 even-odd, 504 finding exact value of a trigonometric expression using, 419 Fundamental finding values of trigonometric functions using, 417–419 solving trigonometric equations using, 497–498 Pythagorean, 419 quotient, 417, 504 reciprocal, 417, 504 trigonometric. See Trigonometric identities Identity function, 102–103 limits of, 946 Identity matrices identity matrix In, 803 multiplication with, 803 Identity property of matrices, 803 Imaginary axis in complex plane, 627 Imaginary numbers, pure, A59 Imaginary unit i( ), A58 Implicit form of a function, 68 Improper fractions, 813 Improper rational functions, asymptotes and, 240–241 Inclination, 411 Increasing functions, 90–91, 93 linear, 142 Independent variable, 66 Index/indices column, of a matrix, 770, 795 of the principal nth root, A87 row, of a matrix, 770, 795 of the sum, 860 Induction, mathematical, 894–898 Extended Principle of, 897 Principle of, 894 proving statements using, 894–896 Inequalities combined, solving, A81–A82 graphs/graphing of, A4–A5 interval notation and, A77–A78 involving absolute value, A82–A83 involving quadratic functions, 179–183 multiplying by a negative number, A79 multiplying by a positive number, A79
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