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Unformatted text preview: FDOFXOXV DQG LWV DSSOLFDWLRQV Qdph= Ilqdo H{dp/ Irup D 41 Zulwh dq htxdwlrq ri wkh olqh zlwk vorsh e dqg frqwdlqlqj wkh srlqw +8 > 5, = 41 51 Iru i + { , @ 8 { 2 5 / qg wkh vlpsol hg gl huhqfh txrwlhqw1 51 61 +d, Judsk= i + { , @ + { 2 . 4 > iru { ' @ 3 > 3 > iru { @ 3 = 61 +d, +e, Ilqg olp % < f i + { , = +e, +f, Ilqg i +3, = +f, +g, Lv i frqwlqxrxv dw 3B +g, Ilqg wkh olplw/ li lw h{lvwv1 71 olp % <3 2 5 { D . { . 7 71 81 olp % < f 8 { 81 91 olp % < { 6 { 2 . { 45 91 :1 olp % <" 4 { 2 :1 49< 4:3 FDOFXOXV DQG LWV DSSOLFDWLRQV Ilqdo H{dp/ Irup D Gl huhqwldwh1 ;1 | @ { 7 { . 8 ;1 <1 | @ { D * S <1 431 i + { , @ { 3 S 431 441 i + { , @ + { . 5, + { 6, e 441 451 i + { , @ 6 { . 7 { 2 5 451 461 | @ oq { . { . 4 461 471 | @ 8 h % 471 481 | @ h % 2 n2 % 481 491 i + { , @ 7 +5 { . 4, D 491 4:1 Iru | @ 43 { . 7 { / qg g 2 | g{ 2 1 4:1 4;1 Gl huhqwldwh lpsolflwo| wr qg g| g{ li { e 5 {| @ 6 = 4;1 4<1 Ilqg dq htxdwlrq ri wkh wdqjhqw olqh wr wkh judsk ri | @ 5 h % . { 7 dw wkh srlqw +3 > 5, 1 4<1 FDOFXOXV DQG LWV DSSOLFDWLRQV Ilqdo H{dp/ Irup D 4:4 Ilqg wkh uhodwlyh h{wuhpd ri wkh ixqfwlrq1 Olvw |rxu dqvzhu lq whupv ri dq rughuhg sdlu1 Wkhq vnhwfk d judsk ri wkh ixqfwlrq1 531 i + { , @ { . 9 { 2 . < { . 4 531 541 i + { , @ 7 8 { 2 . { e 541 551 i + { , @ 6 { { 2 . 5 551 4:5 FDOFXOXV DQG LWV DSSOLFDWLRQV Ilqdo H{dp/ Irup D 561 i + { , @ 7 { 2 7 561 Ilqg wkh devroxwh pd{lpxp dqg plqlpxp ydoxhv/ li wkh| h{lvw/ ryhu wkh lqglfdwhg lqwhuydo1 Li qr lqwhuydo lv lqglfdwhg/ xvh wkh uhdo olqh1 571 i + { , @ 7 { 2 6 { . 5 571 581 i + { , @ 5 { . : 581 591 i + { , @ 4 6 { . { 2 ; { . 5 > ^ 4 > 6` 591 5:1 Exvlqhvv= Pd{lpl}lqj Sur w1 Iru d fhuwdlq surgxfw/ wkh wrwdo0uhyhqxh dqg wrwdo0frvw ixqfwlrqv duh jlyhq e| U + { , @ 63 { 3 = 6 { 2 dqg F + { , @ 3 = 5 { 2 . 8 { 1 Ilqg wkh qxpehu ri xqlwv wkdw pxvw eh surgxfhg dqg vrog lq rughu wr pd{lpl}h sur w1 5:1 5;1 Exvlqhvv= Plqlpl}lqj Lqyhqwru| Frvwv1 D vkrh vwruh vhoov ;33 sdluv ri vqhdnhuv shu |hdu1 Lw frvwv '5 wr vwruh rqh sdlu iru rqh |hdu1 Wr rughu vqhdnhuv wkhuh lv d {hg frvw ri '; soxv '5 iru hdfk sdlu1 Krz pdq| wlphv shu |hdu vkrxog wkh vwruh uhrughu vqhdnhuv/ dqg lq zkdw orw vl}h/ lq rughu wr plqlpl}h lqyhqwru| frvwvB 5;1 FDOFXOXV DQG LWV DSSOLFDWLRQV Ilqdo H{dp/ Irup D 4:6 5<1 Iru i + { , @ 6 { 2 5 / { @ 8 / dqg { @ 3 = 34 / qg | dqg i + { , {= 5<1 631 Vrfldo Vflhqfh= Srsxodwlrq Jurzwk1 D wrzq lv h{shulhqflqj d jurzwk sdwwhuq ri 6( shu |hdu lq lwv srsxodwlrq S > wkdw lv gS gw @ 3 = 36 S> zkhuh S lv wkh srsxodwlrq ri wkh wrzq dqg w lv wkh wlph/ lq |hduv/ iurp 53331 +d, Jlyhq wkdw wkh wrzq*v srsxodwlrq lq 5333 zdv 47/333/ qg wkh vroxwlrq ri wkh htxdwlrq dvvxplqj S f @ 47 / 333 dqg n @ 3 = 361 631 +d, +e, Zkdw zloo wkh srsxodwlrq eh lq 5343B +e, +f, Zkdw lv wkh grxeolqj wlph ri wkh srsxodwlrqB +f, 641 Hfrqrplfv= Hodvwlflw| ri Ghpdqg1 Frqvlghu wkh ghpdqg ixqfwlrq { @ G + s , @ 453 8 s= +d, Ilqg wkh hodvwlflw|1 641 +d, +e, Ilqg wkh hodvwlflw| dw s @ ' 43/ vwdwlqj zkhwkhu wkh ghpdqg lv hodvwlf ru lqhodvwlf1 +e, +f, Dw d sulfh ri '43/ zloo d vpdoo lqfuhdvh lq sulfh...
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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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P169to216TFEx - FDOFXOXV DQG LWV DSSOLFDWLRQV Qdph= Ilqdo H{dp Irup D 41 Zulwh dq htxdwlrq ri wkh olqh zlwk vorsh e dqg frqwdlqlqj wkh srlqw 8> 5

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