ࡱ> SUR~%` o+bjbj :̟̟##Kdddddddx000880$\1tx_f17"7777&7 7eeeeeee$ghhjNfd77777fdd77f>>>7Pd7d7e>7e>>W^_dda71 0=\0J:>_"d/f0_f_k<kDakda77>77777ffB>d777_f7777xxx % xxx%xxxdddddd 8.4 Definite & Indefinite Integrals There are 2 types of integral Indefinite, in which we aren't given the limits of integration, i.e. x=a to x=b, so we just calculate a generic, all purpose solution, and Definite, in which we are told a and b and so we can calculate an explicit value for an area. 8.5 Indefinite integrals If the differential of x3 is 3x2, then SYMBOL 242 \f "Symbol" 3x2.dx = x3 But 3x2 is also the differential of x3  1 and x3 + 8, etc. so that this reversal is not unique  we've 'lost' the constant! So in general, 3x2 is the differential of (x3 + k) where k is any constant this is known as the 'constant of integration'. We write this as: SYMBOL 242 \f "Symbol" 3x2.dx = x3 + k (Later on, youll see that if were given more information, we can work out the value for k, but for now, we just leave it as it is). 8.6 Integration 'magic' Formula Since integration is the reverse of differentiation, for any polynomial y(x) = xn, we can simply reverse the differentiation procedure, so that the integral is given by SYMBOL 242 \f "Symbol" xn.dx = EMBED Equation  + k (except for n = 1) In words: Add one to the power, then divide by the new power. Then add k. Examples 1. SYMBOL 242 \f "Symbol" x2.dx = EMBED Equation  + k 2. SYMBOL 242 \f "Symbol" 20x4.dx = 4x5 + k 3. SYMBOL 242 \f "Symbol" 7x.dx = EMBED Equation  + k 4. SYMBOL 242 \f "Symbol" a.dx = ax + k 5. SYMBOL 242 \f "Symbol" abx3.dx =  EMBED Equation.3  + k 8.6.1 Variations on Nomenclature Because constants dont affect the integration, it is common to bring them in front of the integration sign to make things clearer. For example: SYMBOL 242 \f "Symbol" abx3.dx = ab SYMBOL 242 \f "Symbol" x3.dx = ab EMBED Equation.3  + k or: SYMBOL 242 \f "Symbol" 5q2.dq = 5SYMBOL 242 \f "Symbol" q2.dq =  EMBED Equation.3  + k Also, the position of the .dx is usually last in the line, but it can, in principle, be anywhere inside the integral. You may sometimes see the .dx written first (usually in Physics textbooks). For example: Area = SYMBOL 242 \f "Symbol" dr (r3 r5) This is identical to: SYMBOL 242 \f "Symbol" (r3 r5).dr 8.6.2 Roots follow the same rule 6. SYMBOL 242 \f "Symbol"EMBED Equation .dx = SYMBOL 242 \f "Symbol" x.dx = EMBED Equation  + k 8.6.3 Inverse powers also follow the same rule 7. SYMBOL 242 \f "Symbol" EMBED Equation .dx = SYMBOL 242 \f "Symbol" x3.dx = EMBED Equation  = EMBED Equation  + k This is true so long as the exponent is not 1. SYMBOL 242 \f "Symbol"EMBED Equation  cannot be calculated using this formula because we get a divide-by-zero error. 8.6.4 Other variables 8. SYMBOL 242 \f "Symbol" 2m2.dm = EMBED Equation  + k 9. SYMBOL 242 \f "Symbol" 5EMBED Equation .dSYMBOL 108 \f "Symbol" = EMBED Equation  + k 10. SYMBOL 242 \f "Symbol" EMBED Equation .dSYMBOL 113 \f "Symbol" = SYMBOL 242 \f "Symbol" SYMBOL 113 \f "Symbol".dSYMBOL 113 \f "Symbol" = EMBED Equation  +k 8.6.5 Sums of terms Just as in differentiation, a function can by integrated term-by-term, and we only need one constant of integration. 11. SYMBOL 242 \f "Symbol" 3x2 + 7x.dx = SYMBOL 242 \f "Symbol" 3x2 + SYMBOL 242 \f "Symbol" 7x = x3 + EMBED Equation  + k 12. SYMBOL 242 \f "Symbol"EMBED Equation  + EMBED Equation  + EMBED Equation  + 4x3.dx = EMBED Equation  + x4 +k 8.7 Definite Integrals We now know how to integrate simple polynomials, but if we want to use this technique to calculate areas, we need to know the limits of integration. If we specify the limits x=a SYMBOL 174 \f "Symbol" x=b, we call the integral a definite integral. To solve a definite integral, we first integrate the function as before (i.e. find its indefinite integral), then feed in the 2 values of the limits. Subtracting one from the other gives the area. Example 1. What is the area under the curve y(x) = 2x2 between x=1 and x=3? (Note: this is the same problem we did graphically earlier). Area =  EMBED Equation.2  we write the limits at the top and bottom of the integration sign =  EMBED Equation.2  we use square brackets to indicate we've calculated the indefinite integral = (18 + k)  (2/3 + k) feed in the larger value, then the smaller, and subtract the two. = 18  2/3 = 171/3 sq. units (compare the approximate value we got graphically of 17). Note: the k's cancel. So when we evaluate a definite integral we can ignore the constant of integration. 2. What is the area under the curve y(x) = 2x3  6x between x = 1 and x = 0? A =  EMBED Equation.2  =  EMBED Equation.2  = (0  0)  (  3) = 2 sq.units  EMBED Word.Picture.6  3. What is the enthalpy of a gas at 20 K given that its heat capacity as a function of temperature is given by C = 2T 2, over the range T = 0 K to 20 K? Youll learn in chemistry lectures that the enthalpy of a gas, H, is given by the area under the curve of heat capacity vs temperature. In most cases, we approximate it by saying that the heat capacity doesn't change much with T, so is in fact a constant. If we take an average value between 0 and 20K of 10K, then C~2102=200JK-1mol-1. In this case the enthalpy is just given by H =  EMBED Equation.2  (with C = constant = 200) =  EMBED Equation.2  = [200T]EMBED Equation  = 200(T2 T1) = 200(30 0) = 6.0 kJ mol-1 However in this question, we are asked for a more accurate answer, and are told C is not constant, its a function of T. So H =  EMBED Equation.2  =  EMBED Equation.2  =  EMBED Equation.2  = (16000 / 3)  0 = 5.3 kJ mol-1 (compare this with the approximate answer we obtained when we assumed C was constant). 4. What is the area under the curve y(x) = EMBED Equation  between x = 1 and x = SYMBOL 165 \f "Symbol"? [This may seem oddhow can you calculate an area up to x=infinity? But if you draw the graph, youll see that although x goes to infinity, the curve is getting closer and closer to the y axis and so the area is getting smaller. So in this case, it is possible to calculate a finite area, even though we are integrating to infinity]. A =  EMBED Equation.2  =  EMBED Equation.2  = [2x1]EMBED Equation  =  EMBED Equation.2  = (0)  (2) = 2 sq.units.  8.8 Negative Integrals Consider the function y(x) = 2x within the limits x = 2 to +1. Lets calculate the area under this curve using the standard procedure: A =  EMBED Equation.2  = [x2]EMBED Equation  = (12)  ( 22) = 3 sq. units What does negative area mean?  EMBED Word.Picture.6  The area A1 = ( 4 ( 2 is below the x axis and is counted as ve. The area A2 = ( 1 ( 2 is above the x axis and is counted as +ve. Therefore it is always a good idea to sketch a curve before you integrate, to see if it goes ve anywhere between the limits. 8.9 Integrals of Common Functions For any function for which the differential has been established, reversal of the process gives the integral. Learn these! 8.9.1 Exponential Functions SYMBOL 242 \f "Symbol" ex.dx = ex + k SYMBOL 242 \f "Symbol" eax.dx = EMBED Equation  + k Example 1. What is the area under the curve y(x) = 3e5x from x = 1 to x = SYMBOL 165 \f "Symbol" ? A =  EMBED Equation.2  =  EMBED Equation.2  = (0)  ( 0.004) = 0.004 sq.units 8.9.2 Logarithmic Functions  EMBED Equation.2 .dx = ln x + k (this is the one we cannot do using the 'magic formula' and is very important in Physical chemistry). SYMBOL 242 \f "Symbol" ln x.dx = x.(ln x  1) + k Example: (From 2nd year thermodynamics) Calculate the work done when an ideal gas is expanded infinitely slowly from a starting volume V1 to a final volume V2. The work done is given by the area under the pressure-volume graph, or: Work = SYMBOL 242 \f "Symbol" p(V).dV Since were told its an ideal gas, we can replace p(V) with nRT/V Work = SYMBOL 242 \f "Symbol"  EMBED Equation.3 .dV, and since n, R and T are constants, this becomes Work = nRT  EMBED Equation.3 .dV. Applying the rule, above: Work = nRT  EMBED Equation.3  = nRT (ln V2 ln V1) Work = nRT ln (V2 / V1) 8.9.3 Trigonometrical Functions SYMBOL 242 \f "Symbol" cos x.dx = sin x + k SYMBOL 242 \f "Symbol" sin x.dx =  cos x + k SYMBOL 242 \f "Symbol" tan x.dx =  ln (cos x) + k Example: What is the area under the curve y(SYMBOL 113 \f "Symbol") = 3sin SYMBOL 113 \f "Symbol" between SYMBOL 113 \f "Symbol" = 0 and EMBED Equation ? A =  EMBED Equation.2  = [ 3 cos SYMBOL 113 \f "Symbol"]EMBED Equation  = ( 3 ( 0.707)  (3) = 0.879 sq.units      Chemistry 1S Calculus I Dr Paul May PAGE  PAGE 59 DFP^d/ 0 5 J K b c d e g j l m n o y z ĽԮԮhTh.A\mH sH  h.AH*]h.Ah.A] h.A5CJ$jh.A5CJ$Uhqfh.Ah.AH*] h.A5 h.A5CJ h.A6h.A\mH sH h.Ah=%&EF/ 0 J K v w _ ` + , $a$gd $ & Fa$gd.A$a$gd.Agd.Agd#+n+   - . / H I J K M N O V W h i  3 4 _ ` e 򸲸 h.A5 h.Ah.A h.A6]hh.Ah.A] h.ACJ$jh.ACJ$Uh.A\mH sH  h.A] h.AH*]h.Ah.AH*] h.A6hTh.A\mH sH h.Ah.Ah.A6]6 , - C D E F G H I J M N ] ^ _ ` c d t u x y         ݘyjWH5 h.AEHU$jWH5 h.ACJUVmHnHuh.Ah.AH*]hTh.A\mH sH jBH5 h.AEHU$jBH5 h.ACJUVmHnHujh.AUh.Ah.A] h.A6 h.ACJ$jh.ACJ$Uh.Ah.Ah.A6H*/, e | } ~    E F $a$gdgdgd`gd.A0>&$d%d&d'd+D/NOPQgd.A 1 2 3 5 6 7 8 9 : > ? @ C D I J ` a b c d e f g l m | } ~  쾶셶hj3h.A6<jnH5 hj3h.A<EHU-jnH5 hj3h.A<CJUVmHnHuhj3h.A<jhj3h.A<Uh.Ah.A6]h.Ah.A]h.Ah.AH*] h.A6h.Ajh.ACJ$U h.ACJ$4 L`³کysysnd\nWnysy h~X]h.Ah~X]h.Ah~XH*] h~X6 h~XCJ$jh~XCJ$UhYh~Xhhh~XCJaJhhCJaJh*{hj3h.A6<jhj3hFR<EHU.j? L hj3hFR<CJUV_HnH tH hj3h.A<jhj3h.A<U h.A6h.Ah.A]h.A"yz=>OP ygdFR$a$gdFRgd.Agd$a$gdYgd`   012345678<=STUVWXY[]^qķߠxpjhYUh.AhY]hY hYCJ$jhYCJ$U hY] hYH*] hY6jh~XCJ$Uh~Xh~X]j0h.Ah~XEHU%jc L h~XCJUV_HnH tH jh~XUh.Ah~X]h~Xh.Ah~XH*] h~X6 h~XCJ$(qrstwxyz <=STjkmnopqrstvw¾ӷӷӭqdVhYhYH*aJmH sH hY6]aJmH sH hY6\]aJmH sH hYhYH*aJhY6]aJhYhY6]aJhYhYaJ hYCJ$jhYCJ$U hY6]hh~XhYh.A] hY6hYjhYUj[h.AhYEHU%jLd L hYCJUV_HnH tH wxǽǯЂwsh]VRHBH h.ACJ$jh.ACJ$Uh.A h.A56hh.ACJaJhhCJaJhYhYhYmH sH hYhY6]aJ hYaJhYhYH*aJmH sH hY6]aJmH sH hY6\]aJmH sH hYhYH*aJhY6]aJhYhYaJ hYCJ$jhYCJ$UhYaJmH sH hYhYaJmH sH      +,-./01278GHIJMNPWfk󽷽ǭzodo󽷽hhFRCJaJhh.ACJaJhhCJaJjhFRhFREHU%j? L hFRCJUV_HnH tH hFRh.A]hFRhFRH*] h.ACJ$jh.ACJ$U h.A6h.Ah.A]jH5 h.AEHU$jH5 h.ACJUVmHnHuh.Ajh.AU&  69:վȪՒzg[jH5 h.AEHU$jH5 h.ACJUVmHnHuhThFR\mH sH jH5 h.AEHU$jH5 h.ACJUVmHnHu hFRH*hFRhFRH*\mH sH  h.ACJ$jh.ACJ$U h.A6hFRh.A]h.Ajh.AUjH5 h.AEHU$jH5 h.ACJUVmHnHu#:;?@VWXghij ĸﴩyqijhFRUhFRhFR]hFRCJEH hFRCJ$jhFRCJ$U hFR6hhFRCJaJhCJaJhhCJaJhFRjH5 h.AEHU$jH5 h.ACJUVmHnHujh.AU h.ACJ$jh.ACJ$Uh.AhThFR\mH sH "    ,-./0?@ABDE[\abqrstwx~թՈ~g,jKY; hFRCJOJQJUVmHnHuj hFREHU,jKY; hFRCJOJQJUVmHnHuj[ hFREHU,jKY; hFRCJOJQJUVmHnHu hFRCJ$jhFRCJ$U hFR6hFRjhFRUjH5 hFREHU$jH5 hFRCJUVmHnHu$yz234IJHI:; i`gdFRgd`$a$gdFRgdgdFR+,-.014;IJ鰣铈~vhFRhFR]hFRhFRH*]hhFRCJaJhhCJaJ hFR6jhFRhFREHU%j@ L hFRCJUV_HnH tH hFRhFRH*hFRhFRH*\mH sH  hFRCJ$jhFRCJ$UhFRjhFRUj$ hFREHU.  "#$%&+,-01@ABCFGMNdefuvwx{|qejH5 hFREHU$jH5 hFRCJUVmHnHujhFRUjH5 hj3hFR<EHU-jH5 hj3hFR<CJUVmHnHujhj3hFR<Uhj3hFR<hj3hFR<H*]hj3hFR6<hFRhFRH*] hFR6hFRjhFRCJ$U hFRCJ$$¶ձ՟ՒscYNDhj3hFR<CJhj3hFR<H*]hj3hFR6<j4 hj3hFR<EHU-j4 hj3hFR<CJUVmHnHuhj3hFR<jhj3hFR<UhFRhFR]hFRhFRH*] hFR6jH5 hFREHU$jH5 hFRCJUVmHnHuhFRjhFRUjH5 hFREHU$jH5 hFRCJUVmHnHuKPfl/14SBCVWXY뮡뎂j4 hFREHU$j4 hFRCJUVmHnHujhthtEHU%jB L htCJUV_HnH tH hFRhFRH*]hh6]jhFRU hFR6 hFR5hhFR hFREHH*hj3hFR6<3opqrtxz{}TUVW\]^_`bclmpqwx󙏙jhtUhtht6]hthFRhFR6]hFRhFRH*] hFR5hFRhFR>*CJhFRhFR>*CJEHhFRhFR>* hFRCJhFRCJEHhThFR\mH sH  hFR6hFRjhFRU1iuv/0~$$Ifa$gdtl$IfgdFRl$Ifgdtlgd`$a$gdt$@ ^@ `a$gdFRgdFR  z{ӨӨӨӠӘӅ{wrrhrdrrh6hthtH*] ht6hFRjJY; htU$jJY; htCJUVmHnHuj'htUhtht>*hTht\mH sH j4 htEHU$j4 htCJUVmHnHuhtjhtUj9hthtEHU%jB L htCJUV_HnH tH '   +,OPo}$a$gd6`gdtgdt$a$gdt$a$gdFRgdFRVkd$$Ifl0!x9 t644 laytt-.12EFGHRS`cfhȳl_Qh6ht6]mH sH jshthtEHU%jxC L htCJUV_HnH tH h6htmH sH jhtUh6h6mH sH h6h66]mH sH hthtH*(hthtB*H*PJaJnHphtHh6B*PJaJnHphtHhtB*PJaJnHphtHhtht6]h6ht ht6hi|}~춫l`RRhh6H*]mH sH j KY; htEHU$j KY; htCJUVmHnHujhtUhht6mH sH hht]mH sH hh6]mH sH hhtmH sH hh6mH sH h6htmH sH jhth6EHU%jE L h6CJUV_HnH tH h6h6mH sH jh6U &'LMSTWXklmnwxÿr_Sj|4 htEHU$j|4 htCJUVmHnHujh6h6EHU%j\E L h6CJUV_HnH tH j8h6h6EHU%jLE L h6CJUV_HnH tH jhtU ht6hthhtmH sH hh6>*H*mH sH hh6>*mH sH hh6mH sH hh6\mH sH op%& !!#!$!b!c!r!s!!!!$$Ifa$gdjl$Ifgd6l$Ifgdjl$a$gdj3gd6 p`^p``gd6gdt$%JKLMQRabcdmnwx{|  S T ްޠ}}ބx hj6 hj6] hjhj hj36]hjhj6]hj3hjjZ5 h6EHU$jZ5 h6CJUVmHnHujh6U h66 h6ht h66]h6hth6H* ht>*hthTh6\mH sH , !!!! ! !! !!!"!*!+!,!-!/!0!1!@!A!B!C!J!K!^!_!`!a!k!l!n!o!w!wdXj`4 hjEHU$j`4 hjCJUVmHnHuj&hjEHU,jKY; hjCJOJQJUVmHnHu hjH*hjhj6]hThj\mH sH j#hjhjEHU%j7H L hjCJUV_HnH tH j1!hjhjEHU%j,H L hjCJUV_HnH tH hjjhjU!w!!!!!!!!!!!!!!!!!!!!!."/"2"3"F"G"H"I"M"N"O"P"Q"`"a"b"c"h"i"k"l"o"p"q"󨛻ϑzpj]OhjEHU,jKY; hjCJOJQJUVmHnHuhjhjH*]jLhjhjEHU%jrI L hjCJUV_HnH tH jhjUhThj\mH sH  hj6 hj5h hjh6j'hjhjUh6hjhjhj>*,!!!!!!-"."""""""#I#$a$gdj$a$gdgdjgdgd6VkdXL$$Ifl0, !\  t<644 la<ytjq"r"u"x"y"z"|""""""""""""""""""""""##########!#&#+#,#B#C#D#H##ѧ~h}h}H*]h}h}6\mH sH h}hj6] jhj h}H*j@KY; hjU$j@KY; hjCJUVmHnHujIhjU hj6 h}5 hj5hjhj5\mH sH h}hjhjhjH*].I#J######j$k$$$$$$$z2 &$d%d&d'd+D/NOPQgd}2` &$d%d&d'd+D/NOPQgd}gd_zgd}gdgd`$a$gd}gdj########k$r$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$޾牫牘n$j4 h}CJUVmHnHujh}U h}h}h}h}]h}h}6h}h}6H*]h}h}6]h}h}CJ$jh}CJ$Uh_zh}CJaJh_zh_zCJaJ h}5hh}hFRhjhTh}\mH sH +$$$$$$$$$$%*%+%,%-%2%3%4%5%6%<%=%E%G%I%J%`%a%f%g%j%k%~%%%%%%%%Ŵᎁn$jd4 h}CJUVmHnHujQh}h}EHU%jJ L h}CJUV_HnH tH h}h}6H*]h}h}H* h}h}6H*\]mH sH h}h}6] h}6 h_z6h}h}6h} h}h}jh}Uj4 h}EHU'$$$$$$%%d%e%%%%%%%%&&&&&{&2l &$d%d&d'd+D/NOPQgd}gd_zgd}%%%%%%%%%%%%%%%%%&&&& & &&&|&}&&&&&&&&&&&&&&&&&&&·褘萋{{苐v h}] h}CJ$jh}CJ$U h}6h}h}]jz4 h}EHU$jz4 h}CJUVmHnHuh_zh}CJaJh_zh_zCJaJ h}5h}h}>*\hTh}\mH sH h}jh}Ujd4 h}EHU,{&|&&&&&&Y'Z'''''(((((())+),)`gd{2@&$d%d&d'd+D/NOPQgd}gd}&&&&@'A'B'U'V'W'X'Y'Z''''''''''''''(((( (((((((2(3(4(5(ɿxmxmh~Xh{CJ,aJ,jh~Xh{CJ,UaJ,h{h{aJh{6]aJh{h{6]aJh{h{\aJmH sH  h{aJ h{CJ$jh{CJ$Uh{h}h}h}]h}h}H*]h}h}6 h}]h{h{H*] h{](5(6(I(J(K(L(N(O(X(b(c(d(f(j(l((((((((ҽ𷫢y]@9jh{6B*PJU\]aJmH nHphsH tH6h{h{6B*PJ\]aJmH nHphsH tHh{6\]aJmH sH h{h{\aJmH sH h{h{h{aJh{6]aJh{h{6]aJ h{aJ(jSh{h{EHU\aJmH sH %jL L h{CJUV_HnH tH h{\aJmH sH jh{U\aJmH sH (((((((((((((((Բzqm_Q8-h{\aJmH sH 0h{h{B*PJ\aJmH nHphsH tHh{6\]aJmH sH h{h{\aJmH sH h{h{h{aJh{6]aJh{h{6]aJ h{aJ9jh{6B*PJU\]aJmH nHphsH tHCjUh{h{6B*EHPJU\]aJmH nHphsH tH%j`M L h{CJUV_HnH tH 0h{6B*PJ\]aJmH nHphsH tH(((((((((())) ) ))))))")#)ҽ寡rV*\hT jhSPj^hSPhSPEHU%j_ L hSPCJUV_HnH tH hThSP\mH sH j=\hSPhSPEHU%j^ L hSPCJUV_HnH tH jhSPUhSP hSP6hg%jhg%UjzZhg%EHU,jKY; hg%CJOJQJUVmHnHu#++++++!+"+#+$+&+'+)+*+,+-+/+S+T+U+[+\+]+_+`+f+g+i+j+k+m+n+o+¾h0JmHnHu h0Jjh0JUhhV3hCJOJQJhljhlUh}jwhEdhl<Uhg% hg%hg%j`hg%hg%UhSPhg%>*\hSPhSP>*\ hT>*\ +!+#+%+&+(+)+++,+.+/+S+T+]+^+_+k+l+m+n+o+ &`#$gd<gd`gdg%800P4:p/ =!"#$% 0Dd 0b  c $A? ?3"`?2z18xS!a)xYZVD`!N18xS!a)xYZ kdxcdd``a 2 ĜL0##0KQ* Wä,d3H1)fYK؁(sC0&dT0pE1At 2Bar`r,;f;35V ZZǰb@`E,LF]F\'S~3 1c^Dd b  c $A? ?3"`?2?;˱rP`!?;˱rPԸ 8>(+xڝS+agy)kWRG*)v)EEܶu =88+%'eP13Y9୷~g~kflLhyjĵ)B" LuT6y]Jh@!)@ `PSc 9o7yzPn(бtl wϫׅBk-s[t>cszerWTQ$Hw|b5?G'/SqykOtmR0˼ux>q]F\8KƐniRYb~b_o@UyN.2lf_8xP՗/Qo]݇VglaG4-s>mÜ8SZ#ZIH(VQgM7 A */)>Dd{4 h@0  # A 2;ױ_ `gk773@婹 1",ȁt)X5\֫odq6ίR[~83?e}ume-F+m9ûK}gOÞxVe%J0<>yދ"g<9Io,\B\bŝ^z$N,;l:6WF۰|H3ԫZ}-Dd b  c $A? ?3"`?2 ,Y8LYƕ6/S`! ,Y8LYƕ6  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIKLMNOPQFTXtWYZ[]\_^a`bcedfhgijklmnqopsrvuwxyz{|}~Root Entryc F D\VData JyWordDocumentb:ObjectPoole@8\ D\_898254914F@8\@8\Ole PIC LMETA   "%'*,-./012479<?BEHKNPQRSTUWZ^`abcdefghijklmnpstvwz|}~L t .1  `&@  & MathType "-<@<;Times New RomanP- 2 x 2 n Times New Roman- 2 np Symbol- 2 l+{Symbol- 2 + Times New RomanP- 2 1pTimes New Roman- 2 1 2 T(~ 2 )~ & "Systemn- FMicrosoft Equation 2.0 DS EqCompObj fObjInfoOle10Native dEquation Native Tuation Equation.29q` x n+1 (n+1)`@8lJ qJlJ x n+1 (n+1)L{h_898254935$F@8\@8\Ole PIC  LMETA {  .1   @& & MathType "-<@<Times New Romanl- 2 lx Times New Roman- 2 A3pTimes New Romanl- 2 3 & "Systemn- FMicrosoft Equation 2.0 DS Equation Equation.29q` x 3 3(lJ qJlJ x 3 3CompObj!fObjInfo#Ole10Native$dEquation Native &D_898254958F@8\@8\Ole (PIC )LMETA +LNN  .1   & & MathType "-<@<Times New Roman%- 2 T7 2 2 Times New Roman- 2 2pTimes New Roman%- 2 2x & "Systemn- FMicrosoft Equation 2.0 DS Equation Equation.29q` 7x 2 2P&YesP#>?CompObj3fObjInfo5Ole10Native6dEquation Native 8D(lJ qJlJ 7x 2 2 FMicrosoft Equation 3.0 DS Equation Equation.39q>08, abx 4 4_1275805587SF@8\@8\Ole :CompObj;fObjInfo =Equation Native >L_1275814845F&#F@8\@8\Ole @CompObj"$Af FMicrosoft Equation 3.0 DS Equation Equation.39q>(8*, x 4 4 FMicrosoft Equation 3.0 DS EqObjInfo%CEquation Native DD_1275814988(F@8\@8\Ole FCompObj')GfObjInfo*IEquation Native JH_898254981C-F@8\@8\uation Equation.39q>,8*, 5q 3 3LW|TW  .Ole LPIC ,/MLMETA OCompObj.1Vf1   `&  & MathType0 "-fHJy  "-Ry-X&X&XTimes New Roman- 2 Px & "Systemn- FMicrosoft Equation 2.0 DS Equation Equation.29qObjInfoXOle10Native02YDEquation Native [4_12758056675F@8\@8\@  x lJ qJlJ  x L  ^B  .Ole \PIC 47]LMETA _CompObj69of1   &` Y & MathType-}@}}a -i- O~O~O$ }}D Times New Roman- 2  x 2 x Times New Roman- 2 ?3p 2 ?2p 2 ?y3pTimes New Roman- 2 3 2 2 2 2 2 '3 Times New Roman- 2 ?P/>Times New Roman- 2 T(~ 2 /k 2 `)~Symbol- 2 l= & "System-&(#(&#&#6#!  FMicrosoft Equation 3.0 DS Equation Equation.39q x 3/2 (3/2)=2 x h3 3P" P->H,, x 3/2 (3/2)     =   2 x 3 3ObjInfoqOle10Native8:rEquation Native u_898255000=F@8\@8\Ole xPIC <?yLMETA {CompObj>AfL{Ehl{E  .1  @& & MathType "-@Times New Roman%- 2 i1 Times New Roman-- 2 A3pTimes New Roman%- 2 lx & "Systemn- FMicrosoft Equation 2.0 DS Equation Equation.29q` 1x 3eMaObjInfoOle10Native@BdEquation Native @_898255014;KEF@8\@8\$lJ qJlJ 1x 3L 3 .1   & & MathType "-<@<rTimes New Roman `- 2 lOle PIC DGLMETA pCompObjFIfx Symbol- 2 @-{Symbol- 2 o- Times New Roman- 2 2pTimes New Roman `- 2 2 & "Systemn- FMicrosoft Equation 2.0 DS Equation Equation.29qObjInfoOle10NativeHJdEquation Native H_898255019MF@8\@8\` x -2 -2,lJ qJlJ x -2 -2LNElOle PIC LOLMETA CompObjNQfNE  .1  & & MathType "-@Times New Roman- 2 j$1 2 T2 Times New Roman- 2 2pTimes New Roman- 2 2x & "Systemn- FMicrosoft Equation 2.0 DS Equation Equation.29q` 12x 2P&YesP#(lJ qJlJ 12x 2ObjInfoOle10NativePRdEquation Native D_898255027+UF@8\@8\Ole PIC TWLMETA CompObjVYfLElE  .1  &@ & MathType "-@4Times New Roman- 2 h`1Times New Roman- 2 lx & "Systemn- FMicrosoft Equation 2.0 DS Equation Equation.29q@ 1xlJ qJlJ 1xObjInfoOle10NativeXZDEquation Native 4_898255040]F@8\@8\Ole PIC \_LMETA CompObj^afL  .1   @& & MathType "-<@<Times New Roman- 2 T2 2 A3 Times New Roman- 2 ?3pTimes New Roman- 2 m & "Systemn- FMicrosoft Equation 2.0 DS Equation Equation.29q` 2m 3 3eMa(lJ qJlJ 2m 3 3ObjInfoOle10Native`bdEquation Native D_995707866meF@8\@8\ FMicrosoft Equation 2.0 Equation Equation.29q@  l  Ole CompObjdfcObjInfogOle10NativeD_995707867jF@8\@8\Ole CompObjikcObjInfol FMicrosoft Equation 2.0 Equation Equation.29q` 10 l 3 3B FMicrosoft Equation 2.0 Equation Equation.29qOle10Natived_995707868hoF@8\@8\Ole CompObjnpcObjInfoqOle10Natived_12758058463tF@8\@8\Ole ` 1 q q\. FMicrosoft Equation 3.0 DS Equation Equation.39q q 1/2 1/2=2 CompObjsvfObjInfoOle10NativeuwEquation Native q &Nov#PCancel jP>mx.,  1/2 1/2    =    2  LN_898255081[zF@8\@8\Ole PIC y|LMETA N  .1   & & MathType "-<@<Times New Romanm- 2 T7 2 2 Times New Roman- 2 2pTimes New Romanm- 2 2x & "Systemn-CompObj{~fObjInfoOle10Native}dEquation Native D FMicrosoft Equation 2.0 DS Equation Equation.29q` 7x 2 2generated (lJ qJlJ 7x 2 2_898255088F@8\@8\Ole PIC LMETA   "$%&'()*,/146789:;<=>?@ABDGHJMOPQRSTUVWXYZ[]`cefghijklmnopqrtwz|LW|TW  .1   `&  & MathType0 "-fHJy  "-Ry-X&X&XTimes New Roman- 2 Px & "Systemn- FMicrosoft Equation 2.0 DS Equation Equation.29q@  x lJ qJlJ  x CompObj fObjInfo Ole10Native DEquation Native 4_898255093xcF@8\@8\Ole PIC LMETA L{Ehl{E  .1  @& & MathType "-@Times New Roman- 2 j1 Times New Roman- 2 =2pTimes New Roman- 2 lx & "Systemn- FMicrosoft Equation 2.0 DS Equation Equation.29q` 1x 2$lJ qJlJ 1x 2CompObjfObjInfoOle10NativedEquation Native @_898255098F@8\@8\Ole  PIC !LMETA #LNElNE  .1  & & MathType "-@Times New Roman- 2 jN5 2 T3 Times New Roman- 2 :2pTimes New Roman- 2 gx & "Systemn- FMicrosoft Equation 2.0 DS Equation Equation.29q` 53x 2P&YesP#CompObj+fObjInfo-Ole10Native.dEquation Native 0D(lJ qJlJ 53x 2L    .1  ` &@  & MathType "-|._873374143F@8\0:;\Ole 2PIC 3LMETA 5X`_  "-h_-N N N|@||[|O||$ Times New Roman `- 2 T2 2 3 2 {1 2 5 2 9 Times New Roman- 2 >3p 2 >y 3pTimes New Roman `- 2 6x 2 x 2 xSymbol- 2 .- 2 + & "Systemn- FMicrosoft Equation 2.0 DS Equation Equation.29q 2 x 3 3-1x+5x 3 9&s( CompObjCfObjInfoEOle10NativeFEquation Native I,dlJ qJlJ 2 x 3 3-1x+5x 3 9L<<G  .1  &i &_1275806408rF0:;\0:;\Ole KPIC LLMETA NH MathTypeTimes New Roman- 2 2 Times New Roman- 2 /2p 2 cD1p 2 H3pTimes New Roman- 2 ^x 2 Fdx Times New Roman- 2 cQxb 2 Gxb Symbol- 2 c={ 2 ={Symbol- 2 FTimes New Roman- 2 .` & "System-^&G>&G&뿐v v h+h FMicrosoft Equation 3.0 DS Equation Equation.39q>S; 2x 2CompObj\fObjInfo^Equation Native _o_873374380F0:;\0:;\x=1x=3 +" .dxL 9  .1   & & MathType-NTimes New Roman- 2 2 Ole aPIC bLMETA dCompObjsZ2 )3 Times New Roman- 2 _3p 2 d1p 2 r3pTimes New Roman- 2 x 2 k Times New Roman- 2 qxb 2 qxbSymbol- 2 + 2 @ 2 @ 2 k@ 2  2  2 k Symbol- 2 ={ 2 ={ & "System- FMicrosoft Equation 2.0 DS Equation Equation.2m`'>;; 2x 3 3+k[] x=1x=3ObjInfouEquation Native v|_1275806337F0:;\0:;\Ole xL < FMicrosoft Equation 3.0 DS Equation Equation.39q>c8, 2x 3x="1x=0 +" "6x.dxPIC yLCompObj{fObjInfo}Equation Native ~_873374882F0:;\0:;\Ole PIC LMETA HL (  n  .1  @& & MathType-Times New Romant- 2  x 2 x Times New Roman- 2 _4p 2 T2p 2 1p 2 0pTimes New Romant- 2 )[2 2 3Symbol- 2 - 2 @ 2 @ 2 k@ 2 Z 2 Z 2 kZ Symbol- 2 -{ & "System-&:&&v FMicrosoft Equation 2.0 DS Equation Equation.2m`'>';$,; x 4 2-3x 2 [] -10 L`CompObjZObjInfoEquation Native |_995707603 F0:;\0:;\PIC LMETA pCompObjhObjInfo  &WordMicrosoft Word  4  -Times New Roman4-  u"Arial-2 u4-2 ' ?-2 4-1 ' - 2 40' N- 2 41' - 2 42'O-2 4-4 'zOJ-2 K4-3 '-O-2 4-2 'O-2 4-1 'Od- 2 e40'GO- 2 41'O- 2 42'O~- 2 43'aO1- 2 244'- "- "-% bC3]VvI&Hk#C "-- "-AA- "-- "-VV- "-- "-kk- "-- "-- "-- "-- "-&&- "-- "-AO- "-\A\O- "-AO- "-AO- "-vAvO- "-*A*O- "-AO- "-AO- "-CACO-- "-$Avv--Ij"Arial- 2 l4x"Arial-'7s- 2 s4y-'- "- "- %8vv- -- "- "- %P- -- "- $ tC1]GTdyVt- -M"Arial-2 O4area%%%'- "- "- %Z-  -- "- $wXi- - -  FMicrosoft Word Picture MSWordDocWord.Picture.69qOh+'0  @ L X dpxq@> Paul MayNNI Normal.dot Paul MayUREWordDocumentbSummaryInformation(DocumentSummaryInformation8_1275806584F0:;\0:;\ܥhc ekb-=jjjj  1-X>$jjjL&Xjjjj area y x 4 3 2 1 0 -1 -2 -3 -4 2 1 0 -1 -2 NN@+06"&$ :S<*02.&"b a2)0(g(o!viX(0N$@! 2Q| IJe)<'02e'! % <&02 'J %I 2%0(& 2$0(c.&<#02 '   0"0& @!HG0!0& "HG0 0& !$HG00& %HG00& 'HG00& q(HG00& )HG00& R+HG00& ,HG00&,2-HG00&)2-HG00&e'2-HG00&$2-HG00&2"2-HG00&-V-$#00&K+V-$#00&(V-$#00&&V-$#00&#V-$#00& V-$#h0^2"@!g   M@~3 &  r  f 2 0(6 2 0(6 Y"2 0(6 #2 0(6 :%2 0(6 &20((-20()-20(*-20(j,-20(e,-20()-20(0'-20(|$--20(!--,-34679ijk u ]abc ]abc V]abc ]abc uDa -235689;<>?ABDEGHKLOPSTWXZ[]^`adehijk[xr......[%K@Normala "A@"Default Paragraph Font #'+.148<?k k  k k  !"#$%&'()*+k02d0` P@p 0 `  , ^    & X     R -l@HP LaserJet 4LLPT1:HPPCL5MSHP LaserJet 4LHP LaserJet 4L@g,,@MSUDOHP LaserJet 4L?\ad HP LaserJet 4L@g,,@MSUDOHP LaserJet 4L?\ad  1Times New Roman Symbol &Arial"hJ8K8&%!$Paul MayPaul May2Microsoft Word for Windows 95@@@g-P@X%՜.+,0HPdlt |  Chemistry W, L[0Ole PIC LMETA CompObjf  9 .1  `& 2 & MathTypeTimes New Roman- 2 C 2 wdT Times New Roman- 2 T} 2 T}Times New Roman- 2 .``Times New Roman- 2 .1P 2 .^2PSymbol- 2 ? & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q>M8, C.dT TObjInfoEquation Native i_1275807188,F0:;\0:;\Ole  1 T 2 +"L[0  9 .1  `& 2 & MathTypeTimes New Roman- 2 C 2 wdT TiPIC LMETA CompObjfObjInfomes New Roman- 2 T} 2 T}Times New Roman- 2 .``Times New Roman- 2 .1P 2 .^2PSymbol- 2 ? & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q>U8, 200.dT T 1 T 2 +"L``  .Equation Native q_995707658F0:;\0:;\Ole PIC LMETA CompObjfObjInfoOle10Natived1  @&,4 & MathTypep Times New Roman0- 2 9T} 2 9T}`Times New Roman- 2 81P 2 ,2P & "Systemn- FMicrosoft Equation 2.0 DS Equation Equation.29q`  T 1 T 2P#+4JJJ  T 1 T 2JL[0Equation Native P_1275807052F0:;\0:;\Ole PIC LMETA CompObjfObjInfoEquation Native i  9 .1  `& 2 & MathTypeTimes New Roman- 2 C 2 wdT Times New Roman- 2 T} 2 T}Times New Roman- 2 .``Times New Roman- 2 .1P 2 .^2PSymbol- 2 ? & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q>M8, C.dT T 1 T 2 +"_1275807068F0:;\0:;\Ole PIC LMETA L (0 :  .1  @&2 & MathTypeTimes New Roman- 2 n2 Times New Roman8- 2 tA2p 2 0p 2 `20    !"#$%&(+/123456789:;=@CEFGHIJKLMNOQTWZ]_`abcdefghiknqstuvwxyz{|}pp`Times New Roman- 2 .1P 2 .^2PTimes New Roman8- 2 4T 2 XdT Times New Roman- 2 T} 2 T} Symbol- 2 ={ 2 ={Symbol- 2 ?Times New Roman8- 2 .` & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q>sP/, 2T 2T 1 =0T 2 =20 +" .dTCompObjfObjInfoEquation Native _873375356 F0:;\0:;\Ole PIC  LMETA  CompObjZL[ S V .1  `&  & MathType-rTimes New Roman- 2 2 2 )3 Times New Roman- 2 _3p 2 <0p 2 <20ppTimes New Roman- 2 TSymbol- 2 @ 2 @ 2 k@ 2  2  2 k & "System-;T-o(phH FMicrosoft Equation 2.0 DS Equation Equation.2m`'>`&;*; 2T 3 3[] 020SyL{Ehl{E  .ObjInfoEquation Native |_898259461F0:;\0:;\Ole PIC LMETA CompObj'fObjInfo)1  @& & MathType "-@Times New Roman8- 2 k2 Times New Roman(- 2 92pTimes New Roman8- 2 lx & "Systemn-2 FMicrosoft Equation 2.0 DS Equation Equation.29q` 2x 2$lJ(qJmJ 2x 2LVElOle10Native*dEquation Native ,@_1275807788F0:;\0:;\Ole -PIC .LMETA 0CompObj<fObjInfo>VE9 g .1  & & MathType-Times New Roman- 2 kV2 Times New Roman- 2 2p 2 61pTimes New Roman- 2 x 2 `dx Symbol- 2 6Symbol- 2 ?Times New Roman- 2 `.` & "System- FMicrosoft Equation 3.0 DS Equation Equation.39q>L+, 2x Equation Native ?h_1275807799F0:;\0:;\Ole APIC BL21" +" .dxLq8q: Z .1  @& & MathTypeTimes New Roman - 2 2 Times New RomanMETA DCompObjPfObjInfoREquation Native Sc- 2 t2p 2 1pTimes New Roman - 2 x 2 dx Symbol- 2 t-{ 2 Symbol- 2 ?Times New Roman- 2 .` & "System-ic^ l h D FMicrosoft Equation 3.0 DS Equation Equation.39q>G8, 2x "21" +" .dx FMicrosoft Equation 2.0 Equation Equation.29q_995707870F0:;\0:;\Ole UCompObjVcObjInfoX@  1Ln9 d .1  &`^ &Ole10NativeYD_873375840 F0:;\0:;\Ole [PIC   \LMETA ^CompObj jZObjInfolEquation Native m\ MathType-]]Symbol9- 2 - 2 @ 2 @ 2 _@ 2  2  2 _ Symbol- 2 Times New Roman- 2  2 Times New Roman- 2 B1pTimes New Roman- 2 x & "System- FMicrosoft Equation 2.0 DS Equation Equation.2m@'>&;*; -2x[] 1New Roma? $   & !"#%'()*+-,./021436578:9;=<>@ABCDE{|GHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz}_1275808114F0:;\0:;\Ole oPIC pLMETA rL< <: Z .1  &i & MathTypeTimes New Roman- 2 @2 Times New Roman- 2 c2p 2 1pTimes New Roman- 2 x 2 DdxTimes New Roman- 2 .` Symbol- 2 c>-{ 2 I+{Symbol- 2 F] & "System- FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj~fObjInfoEquation Native Z_995707890PF0:;\0:;\>>X/d 2x.dx "2+1 +" FMicrosoft Equation 2.0 Equation Equation.29q@  -21Ole CompObjcObjInfoOle10NativeDL C   FMicrosoft Word Picture MSWordDocWord.Picture.69qOh+'0 _995707712 F0:;\0:;\PIC LMETA    CompObjh   &WordMicrosoft Word    -Times New Roman- - "- $__ "--- "- $$_""`--Sb#"Arial -2 c#-4 'b-2 c-3 'b-2 c-2 'bO-2 cO-1 'b- 2 c0'Bb- 2 c1'b- 2 c2' b- 2 c3'mbG- 2 cG4'r;K -2 L -8 '3;  -2  -6 '; -2  -4 '; -2  -2 'w;Q- 2 R0'9;- 2 2';- 2 4';- 2 6'|;V- 2 W8'- "- "-% 0Z":{DE Oe--- "-$\`#!-- "-Z0O0- "-ZO- "-ZO- "-Z\O\- "-ZO- "-Z$O$- "-ZO- "-ZO- "-ZOOO- "-Z0Z;- "-0;- "-0;- "-0;- "-_0_;- "-!0!;- "-0;- "-0;- "-e0e;-- "-$0_O_--f-\"ArialT- 2 /\x"Ariala-';- 2 y-'- "- $B_G_ "- %B_G_-  -- "- "- %Y+- -- "- "- %2j1j- -g2@ - 2 A 2'd)7"Arial- 2 8A"Arial$- 'E- 2 1'=w - 2 x A- 'Wv"Arial- 2 y"ArialNe- 2  = 2 - 2 7x- '-ObjInfo"WordDocumentSummaryInformation(!#DocumentSummaryInformation8ܥhc e4Yjjjj !1,...-[/RX$! !,jj,,,jl,,Yjjjj,,, y = 2x A 1 A 2 y x 8 6 4 2 0 -2 -4 -6 -8 4 3 2 1 0 -1 -2 -3 -4 NN@!@!220(P+!g210(#G(200(~#(2/0(''2.0('@'<-02(9#  <,02v& "x (w <+02['((Q~2*0(%H!2)0(?.&<(02' 0'0&!#650&0&N$650%0&z%650$0&&650#0&'650"0&)650!0&.*650 0&\+6500&,6500&-T,6500&,T,6500&@*T,6500&a(T,6500&&T,6500&$T,6500&"T,6500& T,6500&T,65P0F N$> (Q~Z] -= \0R!#i  h \SQE:R/ # P 20("20($20(3%20(b&20('20(T(2 0(T)2 0(T+2 0(TA,2 0(-,2 0(+,20(*,20(:(,20(Z&,20(d$,20(",20( ,20(,@06|&&, (Q#+@06"'X (QW3459:<=?BCEHIKLNu ]abc V]abc ]abc ]abc V]abc ]abc V]abc uDa4;<>?ABDEGHJKMNPQSTVWYZ\]`adehilmoprsuvxy{|j3 %-K@Normala "A@"Default Paragraph Font  #&)-159<?BEHLPTX[      !"#$%&'()*+,-./012 ;mS#SCs3c# S 1 c    + ]    % W     Q  4@HP LaserJet 4LLPT1:HPPCL5MSHP LaserJet 4LHP LaserJet 4L@g,,@MSUDOHP LaserJet 4L?\ad HP LaserJet 4L@g,,@MSUDOHP LaserJet 4L?\ad 1Times New Roman Symbol &Arial"hJ8K8&+$Paul MayPaul May @ L X dpxJH Paul May6 o>q@ Normal.dot Paul May002Microsoft Word for Windows 95@@@|tP@p9Y+՜.+,0HPdlt |  Chemistry o, LElE:  .1  `&  & MathType-@4Times New Roman- 2 k`1_873376449 3&F0:;\0:;\Ole PIC %(LMETA Times New Roman- 2 Ta 2 `pe Times New Roman- 2 0axpb & "System-^&GF >pu&G FMicrosoft Equation 2.0 DS Equation Equation.2CompObj'*ZObjInfoOle10Native)+dEquation Native \` 1ac axm@'>$';(; 1ae ax.1L    ._1275808471!.F0:;\0:;\Ole PIC -0LMETA 1  @ &  & MathTypeTimes New Roman- 2 "3 2 5 Times New Roman!- 2 1pTimes New Roman- 2 exp(~ 2  ).~`Symbol- 2 - Symbol- 2 Symbol- 2 ?Times New Roman- 2 Px 2 dx & "Systemn- FMicrosoft Equation 3.0 DS Equation Equation.39q>R8, 3exp("CompObj/1fObjInfo2Equation Native n_873377124:5F0:;\0:;\5x).dx 1" +"L`:  .1  &^ & MathType-]]Symbol- 2 - 2 @Ole PIC 47LMETA hCompObj68Z 2 @ 2 _@ 2 f 2 f 2 _f Symbol- 2 -{ 2 Times New Roman- 2 3 2 5 Times New Roman- 2 =5p 2 B 1pTimes New Roman- 2 e Times New Roman- 2 xb & "System- FMicrosoft Equation 2.0 DS Equation Equation.2m`'>';+; -35e -5x [] 1Roman-ObjInfo9Equation Native |_873376634<F0:;\0:;\Ole PIC ;>LMETA CompObj=?ZObjInfo@LElE@  .1  &@ & MathType-."Times New Roman- 2 kN1Times New Roman- 2 ZxSymbol- 2 ? & "System-n-Italic FMicrosoft Equation 2.0 DS Equation Equation.2m@'>\';+; 1x  Equation Native \_1275808997CF0:;\0:;\Ole CompObjBDf FMicrosoft Equation 3.0 DS Equation Equation.39q>"@4 nRTV FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoEEquation Native >_1275809120AUHF0:;\0:;\Ole CompObjGIfObjInfoJEquation Native j_1275809159MF0:;\0:;\>N%, 1V V 1 V 2 +" FMicrosoft Equation 3.0 DS Equation Equation.39q>Q+ lnV[] V 1 V 2Ole CompObjLNfObjInfoOEquation Native m_995707893RF0:;\0:;\Ole CompObjQScObjInfoT FMicrosoft Equation 2.0 Equation Equation.29q@ p4LOle10NativeD_1275813586K\WF0:;\0:;\Ole PIC VYL   !#N:  .1  @&` & MathType Times New Roman- 2 0p 2 4p Symbol- 2 p{ Times New Roman- 2 />Symbol- 2 ? & META (CompObjXZ fObjInfo[ Equation Native  g"System-I FMicrosoft Equation 3.0 DS Equation Equation.39q>K  3sin 0/4 +" .d_1275813778^F0:;\0:;\Ole CompObj]`fObjInfo FMicrosoft Equation 3.0 DS Equation Equation.39q@  op/4N>#8,  0/4Oh+'0 Ole10Native_aDEquation Native ?1TableakSummaryInformation(d/ %dxڭSJAswf׀KBb[1E S|V\#l ,XؤFbM* A,D[; 1"6ympE!νsϙ9 `h@AࣇBB"@_z;}):5 $`B 6O:`qG`R[..6 /(|,ƈbejbƐQ,DXmnᮚsȣ!k$?W;@t>-u:_*kT?fAsu.r{=Mx{;N`\"9WZKܫɓ"9$wWMn[M$:uKX]8]K?M 5.1M--k`D8\ u1`K瀅4| 'ޠzDd b  c $A? ?3"`?2nsT+[>`9Ȋ`!nsT+[>`9Ȋb`\fxcdd`` @c112BYL%bpu#ѝٞPd{` {y 2"`_ (5\c|C(_Ie\"THz1/'lA1ב6P>45rS,8 v 0y{iI)$5!dP"CD$<b@3XxڝDd xb  c $A? ?3"`?2 IW>nA[^}`! IW>nA[^ `\xcdd`` @c112BYL%bpu3/mk0arg dopenR~WBD_d.q Ŏ\tx1?'ll-<!A幠 sq;+KRsePdk 1%J$$If!vh5x59#vx#v9:Vl t065x59aytt`Dd H0b  c $A? ?3"`?2Z1DzqJO-_`!~Z1DzqJO-_@"kLxڥRK@%U AD!:8-68J+FZuvP n Ru^\lr ߏV$Q'KÊ0$I*-ԲOUSXDpH Ni /CÿkJ6~sγGΟtlE,(KNҞU?h, ^v񇟀SMqs(^r7LNar|ڲűOҸhr1Q?}<ӣChOo-o 쀋iF[h"0BG@)qxb/eDd $0b  c $A? ?3"`?29XVe)׊9Dd`!9XVe)׊9DdHD kQxڥRNA};'wƨiaa9)-ib,xDL !Q[YYS*Q{ >R!VFݹbHl䒹}o3dj U84C$A(bTn9Ryvl )>RIE 19Y;Uy/Eo~) [٪a0龪Ϯ(TbAegYrt]:^-W wtVXo'D@4x%=kM#G)-q!g̼(3diA%:'Wc>g; vxu]. lAK̆]h"۝ DYBUl o8c'aDd H0b  c $A? ?3"`?2C°ӝ)O3|`!C°ӝ)O3@"kMxcdd``ed``baV d,FYzP1n:fV! KA?H1Z ժ UXRYloN`A 27)?('UTaŪXkyNB]j mĵɁS%ļH1 M-VK-WMa#7׌1 F37oy0@aڣ 2"AQ"cx=Ca?L,(0\M\6h``#RpeqIj.N= @ ]` "g:TDd 0b   c $A ? ?3"`?2gv)X``!gv)X`e kxڭSK@ҟi8D5fptQ1Vhd].]'\TxwXx}Ҁ%$gC"=B}^^&Ҧμ&`h wƬ ˑ1YVܝwh炻OkB+:vXzͩظ`fO}cqyb%os w  p(O ?POB \9.xOWh-sYL̔%s x] Dxgᡜ9}FS;]ZtIWdn˯?w1+*o*^]D(.zuvP<`S8 W1I6x~Dd [lb # c $A#? ?3"`?"2?#cjuu!`!?#cju`Sjxcdd``nf 2 ĜL0##0KQ* W9URcgbR vP fĒʂT/&`b]F"L LgA,a +L *'] ZZǰb@`G,-b&#.#"ΊJ#n>I3ɞM #R*a0_cc*'^FLP{00i7="'27)?A]+{6$e\t1 b , =tĤ\Y\2C  YilDd b % c $A%? ?3"`?#2rL!`a{D@&#`!rL!`a{D@&@ Xxcdd``.ed``baV d,FYzP1n:&6! KA?H1Z l o깡jx|K2B* R& `[YB2sSRsV\ Ld*F\ L 0<&|gd92"nOjeP{J_2#s/=L {+ssp<"|~sc6^] w"\TN9` v0o8121)W2aPdk υ 5JDd= 0 & # A&$2"ٓGC0؄T&qIR_&`!ٓGC0؄T&qIR2 ȽhxeOK P=(@f֠I2 2pvѠ%52j=x˹A+չ:K$ qQh Ԩ n}&%Z&a ceo?R 0`GN2&7-*fJxIs} byE1v}!$Dd 0 $ # A$&"$]Gӑ mLs#(@=#]Gӑ mLsd#fJq3#xO$a;&qK c#OÂp]F %Y X&, Qai|)i C a0"FIJ!19D22ŶH3FLI~ou_wu>gUWWʲ ٯm7DЙB:tY\[%RHMy+xg "̹G[_DaJD^?,ԴogYjs!BGah iuX7uFjm5<!kdx?;9оo%m#:"Daվ&!%La:[6"[W]P7SV{7}a<㭄{*!k_N%}`gR{+ƨCh/܆1ӉLPSg= o[6"8 茷6"6N3NV~ȟ$x:=guFj5K :c@$u:=zgnw:ݾn_ٙuO^gt:柶qәuOgm\k7[tz^S=lOYg,k8 dzڳw/<'33Зtttt d2L}3d2ȝL&)ϘL&i3Rc2L)Gf|c:ެ9fuzf(љ&[ΰFQ:`@vSI;GoUDgPљhU C)3;UKg0Ag:Hg@ytFUGgzW :C;P?:.3 :㣹]]gْ,KAptf+slx򲝕 iwfFQXs<`Fg0I30 K9m?'8~,5٬]o`fo;` kL&[633M2Qux;a׵љtFaX8lUzgHj~3HΜ3Q(__ʿ7~Kk`R̄i< :3w:̗p<7a%LGߨ d2Fg6̒F2/<ӏ|g?|J` FgXs滗.uma <HgY3ٚ_Ovo_x_|YS,<~4:Loq?|͟z`fH)itљhߖ q3:Ld^}_|ߚL 5:{ox_}w&dHάޙSܕ>ν筍ygMgmjzޙg?|G>6ax3M>vgͥ7jg6/ 3g3ԼҋI8<ύjmjٙ͜gyܥgP>o&565w&O̙xڵ7qRC?SlȄԄX-δ'A¡W[gv67ngt~jδ:ZjGwb{z!3퉩o:sdgzr`_{/]^gO^-ggaO 4CRӓojn_+VNzL;iO 205}Lo/^=CrWgnP㢜 R9E9Agt&?Хg]Agt&_'…ӧ}3Ԡ3H>tmox.9C :L<]Sg@gܙҋO#jtFg~Z`]:#2 AgtttfY>[3pL^-9Y3^'7dΜ,5@ɻI㓙i13/3fk+R΀ pUIgV9Vљx %5~7ZK,::3+Lg@gtΜ`sWFgh^fRΠ3:3 Π33:: v:#2 ΀Π3::dSXAgttH3+^tttFgtj~ :x<l6 t&Τ3Π31e3e1L†;NW܂}΀άi4y Lc,z3"W׵Π331E3 ΀Π3:::3 ΀@WttFg@g@g@g@gtAgfttFg@g@g@g@gtЙ?u (5:#2 ΀΀΀΀ ::33330Ƞ33:::::3 ΀΀΀΀ RΈ :]UUy6ߢ(,ttS-.:iwf:6gڻu]Ag@gPVkH΀tXFgЙX?BvxЙN;p(@4::]gԌFlo?::sA::GUUaN::m4Ag@g:26⺮-tt;!,a ӎdDΈ ::33333:΀ ΀Π3:::::3333333:::::cCg@gtttt&O5 Έ ::33333:Θ ΀΀΀΀ :33333:::::::3ϝ)˲| Ⱥ=: odi{p( n0ЙN;繅΀tu}pYxAg@g>!g65]uFdЙ i ::`inq&;j0Ǜ3mtfFLxAg@g0 Z8 LG(v 7cttFg@g@g@g@gttzgDAgttfo333:΀ ΀Π3:::::3333333:::::::39r3m(pAg@gLvhpUj6_?E]g num33]tf4-<ei33]tG<|Йh ::3΀΀@ n |dGM&:iw&35Msx3-f /L<L&::3@g@gf7+fΈ ::33333:: ΀΀΀΀΀΀ $vFg@g@gttؗlAg@gtttttFg@g@g@g@g@gNo.n]&3EQ ::3MӄGBm,tt&Bgt,2Ag@g"tQ ::3R΀DԠ33;3z-i ̻Z3F::¼Ǐ΀άc<< ::sҽgGn?o #9ijvttRJ͉;#2ـ ΀΀΀΀΀΀ ΀@m@g@g@g@g@g1@g@g`8y33s2tt"(CUU::&XeY ih9::봢k4Mitt yaDg@g#*=f'8Yg@g`,DLl::]X̳33f E333UUf3te8:ޚNG~??yݯm::͆WAta>|K:Cżi~ț\tG?k뿄_~}Ȳ>e,7T},_=թt_E?/r)tzi(wrC\ th/64B{rQWD ]8 tlW $.shګW; t:ndb΀@8 qfeY: :3 ::kn.N:##533333΀΀΀΀΀tEQ_uԙ(yʇx+asw1t:=x1؊90M$5^M6:iae ~AewV)o%tfs!f-s xA~փ'x /EiODo "t!~!VcRDJ$ޙxCsQ0ď7K'5lo3Qh4//vBCa)gMow 1D03p2'Nso+t[ o·_v/ naɴ8SX1ΤV"_kT"͔.ƞm_x+m㞊7D3WS"cg~_||$ؙJ1! /lt"'TY4%V"N:㭄1?+?違bv@g 3 Nt"tƙyAg`wtFg qRΘ!3INtޙǝNoA z/[ubvfym\tfY/tFgciך:^W}>e?3|>tSڳ7;uƲ=ut g f@g@g@g@g@g@g9z5L&Sߦ}g2L)&rg,7dJ<83&dԘL&Sʑqo:e񘽎7gxδtp!Fw8Y4Jgtɖ3lQf$BgΑy3[Ggt&ZUo:PcΫb xЙb-PQtљUf<:3,Tΰ ;c):CF8:3hn0jWld.RgJg(ƆlgeBaZ1h֜ӎj =LM:ۋ&lP㢜q3ՙ3Ը(':kg~k=xQNgAg?tYDg?Gpo_ 5 R9o[7KPΠ3:gyAЙ>w>o?}љ8_XWutFg@g Έ :iFg@g`dϖ{ \>~eutFgV̱2tz3'K#nwuFg@gd&;nZ+GtLgttFgt}*&Y}*튇33:ylҙU@g@gtff+æ3:CI6; LF eYZ> L9<-tt&Zg|D΀ :333Bg[C<_3Q@ڝLML˲t::17Ӻ#O&΀άЙYxʲt~3tttFg@g@g@g@g@g@gtttttttFg@g`{ٰ3"΀ ΀Π3:::::3333333: tƵAgtttttFg@g@g@g@g@g@gtttt%5tFdЙivAg@gLQ:΀DL4P Й`:˲LЙiynT΀DԠ33;#5 Lf^qwp::VLgF΀ά,30/l#i33GnOa<΀Μtّ[Ag@gN%(DRsΈ :c63:::::3333333:::::::33q[q#@g@g@g@g@g@g0y F#hPU΀@a0I"ttVkEY::1?iFg@g ZgNp@΀:Zg@g;Mluf^d2H| qX,6t6΀@0 tz#EQ DLUU#.:0z<΀v^kj=iNU!masb84ΐG1oxi@gw<&t@g@gQg(˲_e߿G1¯_wx$$If<!vh5\ 5#v\ #v:Vl t0<65\ 5a<ytjhDd b ( c $A(? ?3"`?'20Tǂ9M`!0Tǂ`\(+Txcdd``.ed``baV d,FYzP1n:,X,56~) @ k1700817T obIFHeA*ݿ;aR&&ܤua[.OV\ _L; 4AHqy1g2~y6D 6WO`u'$37X/\!(?71!096nQ0jO?A&f)0>&_wan/#E;tlo& *)=h``#RpeqIj.Y= @ ]` "lk9Dd 0 ) # A)(20V'G""c O`!V'G""cJhxcdd``^ @bD"L1JE `x0rYjl < %! `yx&Y 7Ӂ`&0-gbMρث eҊ pwM?br<-&~@2DQF&!X>(+KRs` V6#bDd Tb , c $A,? ?3"`?+2K@E\~;F>UQ`!K@E\~;F>D @ mxcdd``^ @c112BYL%bpu4q$8MNŌLLJ% {:  F0eDd lb / c $A/? ?3"`?.2`F|3gMuHv<S`!4F|3gMuHvx`:xcdd``$d@9`,&FF(`Ts A?dmbf)@ UXRY T,@1[Ar؅,L ! ~ Ay +V}. _&@deV 1FÀ!/($ F.?@l``}Ĥ\Y\C 3'L`Ff~1?eiDd Dlb 0 c $A0? ?3"`?/2CQpUbzB|=P&U`!CQpUbzB|=P&UxڥR=KPjmZH*ѡDp-έQ1֚b(N,nc ]hP . >=r"D3ŕ_D!%IΛ|+У QiچEH$s5Wp hS90÷'p֞#hі9?i2j5nl@vq{{ZWzMo֫'#z j?rwA=RY_Rslc׍|9 i~(>e3x~(IZEXը*BVu}ΐhm?OO,ÕЁjiDd b 1 c $A1? ?3"`?02 >i/._6UX`! >i/._6Uxcdd``dd``baV d,FYzP1n:L ,B@?b X깡jx|K2B* R vf1 @201W&00zÊU7)tiF\Na`v0o8M221)W2,ԡRYO`[Dd D0 2 # A212?\, o-ןJZ`!\, o-ןJ^`!xcdd``^$D@9@, fbd02,( 1dbfaZ d30&dT20l``Y}"Lw,a K"h VDL@(\3H+22 ”~ ! ~ Ay >B&~@2(+KRs`f&%}{Dd b 3 c $A3? ?3"`?22?gc~y\`!?gc~y@x gxcdd``cb``baV d,FYzP1n:&B@?b sC0&dT20L @201d++&1X|#+|-KT T@ZS*x@$s}QI;!2 2Bea{903Yřy0j@gBlROM>L2aF0_= ɏ @F|?1mk5_$s@W&E] UL`s?erA8 E `pddbR ,.Ie2C D$<b@3X?<Dd ,|b 5 c $A5? ?3"`?32bL 6+J^8b>^`!6L 6+J^8b`0xcdd`` @c112BYL%bpuOF,Nd!$ Hΐ ɯHMd: 71{[V35]UkuU}~ݏiǏ{iz4_|M{NO/O/?˓'~y:>O?~_~pxr}y_)쿷OK/^M_ɳ׻?nճwwp8>oL>^ΊbsU=ĥw6ASuΎ.jɥŚnޜ=G5zL+TqiȺI|-A&VP= m;RݍҹGw#nڶäzRzq-ƷauU6N(2*Kz`4Y-N~%^U@Ou4*@.Uy(IK"\% rrK%.5y$PK\҅$PK\.ڪb.5u)•JK8-ia[K#r.]Jy'YCAp M]*])xs-ڋ%^p*3M2wuNٙPݥK2블/|M6mgѡh+fuTK;õwE+s.R>ZBrl=ғK2WU€.] oq)&.Aiq{ P.ԁK{DK)4i(qI%1_ܥĥP.i.qIʻ4O%:K\RUqi&%.9-.KZK\Z.]KP:.K8(qK]:KR.RpҤ4|uNrIǥA긔+Uڼ\:Is@iK:${eXNh PB94:gp䮮Kw4q J\2_:K#_R+.}75$\TYW9? 8.ƀ%%. $K\2$m.qQi $`7̗q#O(q}pBKxhK\RFPZY4hu#Y.u.}mb7°R7󥔱s:KPu\=K븎/ܿtO.u9~Adn(Ҙ.:/4:})cPZqͥ]: ^/m$KΗZPst UqdA%ibR_\ 5_jqCKҽKmt(q|:%.qiݨ?^%.ɀ.KKG$:%.qiJnK4ߛcԁKL̗v+%.qi)S>@K¥8ҎqzH\Z#{/RWKq'EX:K&ۻ.X4K%9l^"E$ uYFz-8\Fpr:P&H+fԭ㺿O̎.IK"bYݿ$"%ᒈHa?MǏW?:~4WO~x?MOޙ?w>?j׿:?=w}î ȄK"\jt#D%ȽK6.J\\\(qK"\\(qK"\|%$z)8K\jѹ$PD䒦@K\=K:D%. D4M\D&.pK"\-4vLӧ7EqɳU8/nƇygg?/u \JiKƴ.ƙϯ2gyvKez`40?"ķ{ǘgwG첕J@.%6!_cѥb'en[̊_\JS\JY;K8\:+ƊU`fUM]:;ʻc뫹7N&kysf~d=K3Pťo#'p\<x`\ 怒%q6\@ upKMtDKRݥnT?WApk&.$ULcL+3fGid-^Q&2YqI%%.b?)LZ4%.2i]2_U0Mc4\qITإ RLq{.ݸZJҤ9F;!މ.9% RO蒁RIP(u0dqݻ94KwBb_&.AiwIǥ/-tKeh PB9ԮK 5pKȋ$7MZJ\R(4$+\J%h.%.s)MJ\.qIΗ,$:J\Rǭv)MK\.qI̗zr)MZJ\R(4qIW4q J\2_:K\vIs@K%.q\ #MJ\t6pKbԺKVsJ}tws.5 %]KФV4q\%2.mIs@K%. %.qIWإ4i(qK\\pi M\n%K8.qIɥ4i(qI%1_:K\R-Ѥ9ԁK_OK\.]|Kh PǥgR4w.]K%h.㸤RIs@iǹ $UKr*uiF'4q)KKϗRNĥD-52BR.5m.Ф9%|ipRh PB9%)Mg]\2;b&.f"vDK""]矿yW|ғǏߘ$$If!vh5 5#v #v:Vl t05 5aytg%Dd > ( # A"@@'"7ʪeW~1-#,J@= ʪeW~1-#, $ $xڕP @SHB!H?XZE K++eOB@ā!ٻ50^nWz`ՀC#5F3:_mqؤt}N7{V]3՜.+,0 hp  University of BristolDocumentSummaryInformation84CompObj"q?#'  CALCULUS Title  FMicrosoft Office Word Document MSWordDocWord.Document.89qL@L >)Normal5$7$8$9DH$CJ_HmH sH tH R@R  Heading 3$<@&5CJOJQJ\aJDA@D Default Paragraph FontRi@R  Table Normal4 l4a (k(No List4@4 Header  9r 4 @4 Footer  9r .)@. V3 Page Numberz@#z l Table Grid7:V05$7$8$9DH$H@2H 1 Balloon TextCJOJQJ^JaJo#%&EF/0JKvw_`+,e|}~EFyz=>O P    y z 2 3 4 I J H I :; iuv/0~   +,OPop%&#$bcrs-.IJjkde{|YZ  !!+!,!-!N!~!!!!!!!!!!""""""# ### #!###%#&#(#)#+#,#.#/#S#T#]#^#_#k#l#m#p#(0000 0 00(0050050505050505050505(00a0a0a0a0a0a0a0a0a0a0a0a0a0a0a0a0a0a0a0a0a(0000000000000(0000(00Q 0Q 0Q 0Q 0Q (00 0 0 0 0 0 0 0 (005 05 05 05 05 05 05 (00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0  0  0  0 0 (0000000000000000(0000(00i0i0i0i0i0i0i0i0i0i0i0i0i0i0i0i0i0i0i0i(000000000000000000000000000000(00-!0-!0-!0-!0-!0-!0-!0-!0-!0-!0-!0-!0-!0-!0-!0-!0-!0-!0-! 0-! 0-! 0-!0@0X00@0X00@0X00@0X00@0@0@0@0@0@0@0@0X00t yz=> %&#$bcrs-.IJdYZ  !!,!!!""""""# ### #p#X00L,LX00KX00X00X00X00X00X00X00X00X00X0 0I |MX00X00,LX000X00LX00X00X00X00X00X00X00X000X00 MX00X00X00X00X00X00\NX00X00X00X00X000X00 OX00X00X00 X00  OX00 X00X00X00X0%0 &8PX0%0 X0%0X00X0)0X00X00X00X00X00X00X00X00X00X00X00X00X00X00 OX00X0<0X0<0X0>0 X0>0 ?RX0>0 X0>0 X0>0X0<0X0>0X0>0X0<0@0 1<JJJM  qw: h w!q"#$%&5(((#))*+o+ !"#$%'()*+-/0134579:<>?@ABDFG, yio!I#${&,)) +o+&,.268;=CEHn+y,CM]_1I`l|~  0<S]qsSj  + 7 G I   ? V W g i  , / ? A D [ a q s ~   + -  " 0 @ B M d e u w { BVX1EGh|~WkmwQac{ !0@BJ^`2FHP`bI`j~| 2 5 I K N!e!!!!!"2"<"S"]"t"~"""""""""""o#999:9:99:99:99:99:999:9:9:9::9:9:9:9:9:9999:999:9::::9::::::::::::9:::::::99:9:::999:::999999::9:18<CFM! !_PictureBullets!#p#"#p#EJ   MQyEG  M O !!4!C!g!j!k!o!!!!!!!!!!!""##!#"#####%#%#&#&#(#)#+#,#.#/#m#p# 0?`pio}P ^ k q 4 ? y{umpk}GJ  -!C!g!j!!!!!""!#"#####%#%#&#&#(#)#+#,#.#/#m#p#333333333333333333333333333333333333333&`3FbP z 4 I -Pbetu.]f| -!N!"#!#"#####%#%#&#&#(#)#+#,#.#/#m#p#!#"#####%#%#&#&#(#)#+#,#.#/#m#p#t,]>A#||b##t+@+?Jg؃iIL423L8/T@?RBWD6*TxaY%!4T]p1?d:"st@T#x~w*^`OJQJo(hH^`OJQJo(hHpp^p`OJQJo(hH@ @ ^@ `OJQJo(hH^`OJQJo(hH^`OJQJo(hH^`OJQJo(hH^`OJQJo(hHPP^P`OJQJo(hHh^`OJQJo(hHh^`OJQJo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJo(hHohPP^P`OJQJo(hH808^8`0o(. ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.h808^8`0o(. ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.h808^8`05o(() ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.@h8^8`)808^8`0o(() ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.h ^`hH.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH.808^8`0o(() ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.h^`OJQJo(hHh^`OJQJo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJo(hHohPP^P`OJQJo(hHh ^`hH.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH.h808^8`0o(() ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.^`OJQJo(hH^`OJQJo(hHpp^p`OJQJo(hH@ @ ^@ `OJQJo(hH^`OJQJo(hH^`OJQJo(hH^`OJQJo(hH^`OJQJo(hHPP^P`OJQJo(hH23L##@?R*T"st?diI!4T]?x~w]>A#2+aY2 @h h^h`OJQJo(%D%z˨H6,sm˺i$[j         f228        f228        f        \                 %                          \         6VRWsV5 ~KnxKl \D2g Q m*)T9sVfOhu?-Us}%4!)$;$c$*%g%&@&>(4](.LM/!2W2g2N3V34:4?46C7 :.[<C@*?BMC-"GzGuBHfH$JdJszNSP' QFR` T`VXKX~X@Zp?[AJ[O]e]r7^1_haiEc9dK^eqf{h1ibk)E_1j3 Ttgcssl _qp}f`Ciom.ANA?QxVRY}<.S x+rxx2;"RR?GIO?08a23"i{6b,8s m5{\N=|VQ V&tNQj P=T{<Ij!S~!kl.GGD0w i0~ P.""## #!#"###%#(#+#.#p# C0  @!!P&!!o#P@UnknownGz Times New Roman5Symbol3& z ArialcCG Times (W1)Times New Roman;SimSun[SO5& zaTahoma?5 z Courier New;Wingdings"1hF6f5f!>?>?4d## 2q XZ ?!#>)2CALCULUScppwmcppwmD