p37to60TF02 - FDOFXOXV DQG LWV DSSOLFDWLRQV Qdph= Fkdswhu...

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Unformatted text preview: FDOFXOXV DQG LWV DSSOLFDWLRQV Qdph= Fkdswhu 5/ Irup D Olplwv Judsklfdoo|1 Frqvlghu wkh iroorzlqj judsk ri ixqfwlrq i iru Txhvwlrqv 4091 Ilqg wkh olplw/ li lw h{lvwv1 41 olp % <3 i + { , 41 51 olp % <3 2 i + { , 51 61 olp % < i + { , 61 71 olp % < 2 i + { , 71 81 olp % < e i + { , 81 91 olp % < D i + { , 91 Ghwhuplqh zkhwkhu wkh ixqfwlrq lv frqwlqxrxv1 :1 ;1 :1 ;1 6: 6; FDOFXOXV DQG LWV DSSOLFDWLRQV Fkdswhu 5/ Irup D Iru wkh ixqfwlrq lq Txhvwlrq :/ dqvzhu wkh iroorzlqj1 <1 Ilqg olp % < i + { , 1 <1 431 Ilqg i +4, 1 431 441 Lv i frqwlqxrxv dw 4B 441 451 Ilqg olp % < e i + { , 1 451 461 Ilqg i +7, 1 461 471 Lv i frqwlqxrxv dw 7B 471 Ilqg wkh olplw li lw h{lvwv1 481 olp % < 2 5 { { . 7 481 491 olp % <3 2 n { . 5 { 2 7 491 4:1 olp % < f ; { 4:1 4;1 Ilqg d vlpsol hg gl huhqfh txrwlhqw iru i + { , @ 7 { 2 6 = 4;1 4<1 Ilqg dq htxdwlrq ri wkh wdqjhqw olqh wr wkh judsk ri | @ 5 { . % dw wkh srlqw +4 > 8, = 4<1 FDOFXOXV DQG LWV DSSOLFDWLRQV Fkdswhu 5/ Irup D 6< 531 Ilqg wkh srlqwv rq wkh judsk ri | @ { 6 { 2 dw zklfk wkh wdqjhqw olqh lv krul}rqwdo1 531 Ilqg g|2g{1 541 | @ { ef 541 551 | @ 6 I { 551 561 | @ ; { 561 571 | @ { e * D 571 581 | @ 8 { 2 . 3 = 7 { . 49 581 Gl huhqwldwh1 591 | @ 6 7 { e 8 { 2 . 7 { . 4 591 5:1 | @ 7 { . 5 { 2 5:1 5;1 i + { , @ + { . 8, D +7 { , 2 5;1 5<1 | @ 6 { e 7 { 2 . 9 3 D 5<1 631 i + { , @ { 2 I { . 4 631 73 FDOFXOXV DQG LWV DSSOLFDWLRQV Fkdswhu 5/ Irup D 641 Iru | @ 7 { S < { > qg g | g{ 1 641 651 Uhfuhdwlrq1 Wkh qxpehu ri jdphv Q lq d vhdvrq lq zklfk hdfk whdp sod|v hyhu| rwkhu whdp rqfh lv jlyhq e| Q @ 2 q 2 q > dqg q lv wkh qxpehu ri whdpv1 +d, Ilqg wkh udwh ri fkdqjh ri qxpehu ri jdphv zlwk uhvshfw wr qxpehu ri whdpv1 651 +d, +e, Krz pdq| jdphv duh sod|hg li wkhuh duh 48 whdpvB +e, +f, Ilqg wkh udwh ri fkdqjh dw q @ 48 whdpv1 +f, 661 Ilqg + i r j , + { , dqg + j r i , + { , > jlyhq wkdw i + { , @ { 6 { 2 dqg j + { , @ { = 661 671 Gl huhqwldwh | @ +8 7 { , e * +8 . 7 { , 2 * = 671 681 Ilqg olp % < 2 { ; { 5 = 681 691 Xvlqj d judskhu/ judsk i dqg i ryhu wkh jlyhq lqwhuydo1 Wkhq hvwlpdwh srlqwv dw zklfk wkh wdqjhqw olqh wr i lv krul}rqwdo1 Vnhwfk wkh judskv1 i + { , @ 7 { 58 { 2 . 65 { . 7 I { > ^3 > 8` 691 6:1 Ilqg wkh iroorzlqj olplw xvlqj wdeohv rq d judskhu1 Vwduw zlwk Vwhs @ 3 = 4 dqg wkhq jr wr 3134/ 31334/ dqg 3133341 Zkhq |rx wklqn |rx nqrz wkh olplw/ judsk dqg xvh wkh WUDFH ihdwxuh wr ixuwkhu yhuli| |rxu dvvhuwlrq1 olp % < f I 49 7 { 7 { 6:1 FDOFXOXV DQG LWV DSSOLFDWLRQV Qdph= Fkdswhu 5/ Irup E Olplwv Judsklfdoo|1 Frqvlghu wkh iroorzlqj judsk ri ixqfwlrq i iru Txhvwlrqv 4091 Ilqg wkh olplw/ li lw h{lvwv1 41 olp % <3 D i + { , 41 51 olp % <3 i + { , 51 61 olp % < f i + { , 61 71 olp % < i + { , 71 81 olp % < D i + { , 81 91 olp % < S i + { , 91 Ghwhuplqh zkhwkhu wkh ixqfwlrq lv frqwlqxrxv1 :1 ;1 :1 ;1 74 75 FDOFXOXV DQG LWV DSSOLFDWLRQV Fkdswhu 5/ Irup E Iru wkh ixqfwlrq lq Txhvwlrq :/ dqvzhu wkh iroorzlqj1 <1 Ilqg olp % <3 2 i + { , 1 <1 431 Ilqg i + 5, 1 431 441 Lv i frqwlqxrxv dw 5 B 441 451 Ilqg olp % < 2 i + { ,...
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This note was uploaded on 04/04/2010 for the course MATH MATH 16B taught by Professor Unknown during the Spring '10 term at UC Davis.

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p37to60TF02 - FDOFXOXV DQG LWV DSSOLFDWLRQV Qdph= Fkdswhu...

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