I4 Subject Index of tangent line to graph of a function, 961–962 transforming between polar and rectangular forms, 606–607 trigonometric, 493–503 inverse, solving, 482–483 involving a single trigonometric function, solving, 493–496 linear in sine and cosine, solving, Sum and Difference Formulas and, 518–520 quadratic in form, solving, 496–497 solutions of, 493 solving using a calculator, 496 solving using a graphing utility, 498 solving using fundamental identities, 497–498 solving using identities, 527–528 in two variables finding intercepts algebraically from, 20–21, 23 in form { } = y x expression in , 5 graphing by plotting points, 4–6 graphing using a graphing utility, 6–8 testing for symmetry, 21–23 of a vertical line, finding, 36 Equilateral hyperbolas, 719 Equilibrium, static, 645–646 Equilibrium point, 144 Equilibrium position, 584 Equilibrium price, 144 Equilibrium quantity, 144 Equity of complex numbers, A59 Equivalent equations, A44–A45 definition of, A44 procedures resulting in, A45 Error triangle, 19 Euler, Leonhard, 302, 392, 629, 932 Euler’s Formula, 629 Euler’s number, 302 Even functions definition of, 87 identifying, 87–89 Evenness ratio, 324 Even-odd identities, 504 Events, 927 complement of, 930 mutually exclusive, 930 probability of, 927 union of, probability of, 929–930 Expanding across a row or column, 788 Expected value, 938 Exponent(s). See also Power(s) base of, A8 fractional, expressions containing, writing as radicals, A91 laws of, 295 Laws of Exponents and, 295, A7–A9 negative, A8 rational factoring expressions containing, A91, A92 simplifying expressions with, A91–A92 relating logarithms to, 313 Exponential equations, 304 quadratic in form,solving, 340 solving, 338–340, 341 solving using logarithms, 319 Exponential form of complex numbers, 629, 631 complex roots and, 633 converting complex numbers between rectangular form and, 628–631 Exponential functions, 294–312 definition of, 296 evaluating, 294–298 fitting to data, 367–368 identifying, 297–298 number e and, 302–304 properties of, 301 solving, 304–305 Exponential law, 355–357 Exponential models from data, 367–368 Exponential probability, 305 of a line finding given two points, 39 general form of, 39–40 linear dependent, 757 independent, 757 in one variable, definition of, A45 solving, A45–A47 solving algebraically, A45–A47 solving equations that lead to, A46–A47 solving using a graphing utility, 31 systems of. See Systems of linear equations of lines parallel, 40–41 perpendicular, 42–43 point-slope form of, 36–37 slope-intercept form of, 37–38 logarithmic, 319–320 solving, 336–338, 341 nonlinear, systems of, 821–831 elimination method to solve, 822–826 historical feature on, 827 substitution method to solve, 821–822 in one variable, A44 of a parabola, 683, 684–687 parametric for a cycloid, 744–745 definition of, 736 graphs/graphing of, 736–738 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 polar. See Polar equations polynomial, solving, 222 quadratic, A47–A48 definition of, A48 solving by completing the square, A50–A51 solving by factoring, A48–A49 solving using the quadratic formula, A51–A53 solving using the square root method, A49 in standard form, A48 quadratic in form, solving, A53–A54 radical, solving, A90 rational, solving, A47–A48 rectangular converting polar equations of conics to, 733 identifying and graphing polar equations by converting to, 611–612 for a plane curve defined parametrically, 738–740 plane curves defined by, parametric equations for, 743–745 roots of, A44 rotation of axes to transform, 721–723 analyzing equations using, 724–725 identifying conics without, 726 satisfying, 4, A44 of a secant line, 96 second-degree, A48 sides of, 4, A44 for sinusoidal graphs, 436 solution sets of, A44 solutions (roots) of, A44 solving, A44–A58 algebraically, A44–A45 by factoring, A54–A55 using a graphing utility, 28–32 systems of consistent, 756 definition of, 755 dependent, Cramer’s Rule with, 790 equivalent, rules for obtaining, 759 examples of, 755–756 inconsistent, 756, 790 linear. See Systems of linear equations nonlinear, 821–831 solutions of, 756, 762 Earthquakes magnitude of, 325 zero-level, 325 Eccentricity of a conic, 729 of a conic section, 703 of an ellipse, 704 of a hyperbola, 719 Eddin, Nasir, 392, 573 Effective rate of interest, 349 Effective rates of return, 348–349 Efficiency at generating life, 599 Elements (Euclid), 573, 883 Elements of a set, A1 counting, 911–913 Elimination Gauss-Jordan, 776 solving a system of linear equations using, 758–760 solving systems of nonlinear equations using, 822–826 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 Ellipsis (...), A3 Ellipsoids, 700 Elongation angle, 568 Empty set, A1 End behavior of graphs of polynomial functions, 198–201 of graphs of rational functions, horizontal asymptotes and, 239 Entries, of a matrix, 795 diagonal, in square matrices, 803 Equality of complex numbers, A59 of sets, 911 of vectors, 637, 641 Equally likely outcomes, 928–929 Equal matrices, 796 Equal sets, 911 Equations absolute value, solving, A54 analyzing equations using, 724–725 approximating solutions to, using a graphing utility, 29–31 of a circle general form of, 51–52 graphing polar equations and, 614–615 standard form of, 48–49 cubic, solution of, 226 Demand, 171, 172, 270 depressed, 220 of an ellipse, 694, 695–697, 698, 699 equivalent, A44–A45 definition of, A44 procedures resulting in, A45 exponential, 304 quadratic in form,solving, 340 solving, 338–340, 341 solving using logarithms, 319 first-degree, A46 as functions, 65 of functions. See Function(s) functions defined by, inverse functions of, 286–289 general, of a conic, 726 of a horizontal line, 37 of a hyperbola, 706–707, 708–710, 711–712, 713–714 identifying conics without, 726 key, graphing, 24–26 x y2 = , 24–25 y x 1 = , 25–26 y x3 = , 24
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