Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%MCS 122 Chapter 1 Review of LimitsSo&e o' the &aterial in these slides is 'ro& Calculus 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%(wo Basi$ )roble&s o' Cal$*l*s(he sol*tion to both o' these proble&s re+*ires the *se o' limitsCalculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%1.1.1(p. 70),i&its -An In'or&al .iew/Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Figure 1.1.9(p. 71)Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%1.1.2(p. 72)0ne1Sided ,i&its -An In'or&al .iew/Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%1.1.3(p. 73)(he 2elationship Between 0ne1Sided and (wo1Sided ,i&itsCalculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Figure 1.1.13(p. 73)Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Exercise 1.1.3(p. 77)Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Exercise 1.1.5(p. 77)Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Figure 1.1.15(p. 74)Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%1.1.4(p. 75)In'inite ,i&its -An In'or&al .iew/Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Exercise 1.1.7(p. 77)Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Exercise 1.1.8(p. 77)Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Exercise 1.1.9(p. 78)Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Figure 1.2.1(p. 80)Cal$*lating ,i&its 3 Basi$ CasesCalculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Theorem 1.2.1(p. 80)Cal$*lating ,i&its 3 Basi$ CasesCalculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Cal$*lating ,i&its 3 Algebra 2*lesCalculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Exercise 1.2.2(p. 87)Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Theorem 1.2.4(p. 85)Cal$*lating ,i&its 3 2ational 4*n$tionsCalculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%1.3.1(p. 89),i&its at In'inity -An In'or&al .iew/Cal$*lating ,i&its 3 As 5 goes to 6,1 In'inityCalculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Figure 1.3.2(p. 89)Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Figure 1.3.4(p. 90)Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%1.3.2(p. 91)In'inite ,i&its at In'inity -An In'or&al .iew/Cal$*lating ,i&its 3 As 5 goes to 6,1 In'inityCalculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Exercise 1.3.1(p. 96)Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Exercise 1.3.2(p. 96)Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Exercise 1.3.4(p. 97)Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Figure 1.4.1(p. 100)Cal$*lating ,i&its 3 2igoro*s De'inition77Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Figure 1.4.2(p. 101)Cal$*lating ,i&its 3 2igoro*s De'inition77Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%e!i"itio" 1.4.1(p. 101),i&it De'initionCal$*lating ,i&its 3 2igoro*s De'inition77Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Cal$*lating ,i&its 3 2igoro*s De'inition772 5 4 lim ) ( lim31 1= + => > x x x fx x"e $an $al$*late that 4ind a n*&ber89s*$h that :'-5/ 3 2: ; %< i'; :51=: ; 8%->se the graphing $apability o' yo*r $al$*lator/ limx>1f (x) = limx>12x3 4x + 4 = 2Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%e!i"itio" 1.5.1(p. 110)Contin*o*s 4*n$tionsCalculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Theorem 1.5.3(p. 113)Contin*o*s 4*n$tionsCalculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Theorem 1.6.5(p. 123)(wo *se'*l (rig ,i&itsCalculus, 9/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright 29 by !ohn "iley # Sons, In$%All rights reserved%Figure 1.6.3(p. 123)(wo *se'*l (rig ,i&its