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# Week 1&2 Notes MATH1431

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This 21 page Class Notes was uploaded by Sebastian Bidegain on Friday January 30, 2015. The Class Notes belongs to MATH1431 at a university taught by Dr.Almus in Fall. Since its upload, it has received 64 views.

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Date Created: 01/30/15

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quotf a if 39 if 5 Ea jag gmlmaeey 7 l f IE 1amp1 E a Q m d EEL mt If Hm 3i while Hm gx UM1en Em 1 gt quot I fgt w l Mquot 3 and Hm 331 2 when E i4 an grew x jgtl x ac g I isIderwmmigrm iwm qmm WT and HIE limit may car may n01 exists Mum wurk is HE EdEd t0 ifnvsstigate this IimiL This situa timn where mam fths intemsting limit p bl ma am Fact If 1 x far 3H J I lE FbUH l t Equal tn than Jim fv Hm xgtc 17 gtL H m thin nf LMx as a Simpl i d wr sinn mquot x 1 WhUSE li n39lit as J C is Easy to datennine Such as a polyn rnial 01M rati na l fmmim Wh numeratar an demminamr d0 mm bath appmach 16 If p and are p0hnmmials wilh q i 390 then p x P t in V a 39 x Example A rational fumtiun Wh damminamr p pt h It while its numemmr dues mm Em mm iim it exists F 7 xg 39 Mari aSH W NE j l Jr s 3 V x5 Wha hm j quotif 3amp5 VI 23 J Eff dtzH er ma 15 I U li l mpl 39i Find I g E a L warm gar35 1T Sum m 113 In gmmal m Eh limit Ufa fun cmn da nad with a fumma we ahamld direm substituti n in Hch get a was numb r than limit is a 7 5quot 3 a l va gm 3 fracti n that Marks like e where a the1n 11w limit dunes mm m we gust a H Em o fthe hm this call d an quotiind ten n nal film Mpg WE need In W fk hardar IE gum a 1MLWhajt limit ism s can be dune by algebraic mmthnds such as ratinnalizing m wing same mm that rueam Simp i ring the given thmtinn Thi fact rimg and cancc ming wmmmn factors techniqma m r 1 6 39 If 11 amsts H 4 M Id M r 17 W U in f y m w a Example Evaluatg Jim 39 f a g L29 1 w WLEE J w W MM a i quot quot r 51b 39 in n if it EKiSTS Examjplj ri Evaiuate Hm I arean llx 2 Mn ml 1 MMquot in we mmpum the limil 0f a piecewise mmi n l5 E F39LQLLmrfg plus A I un utmn Em f L x2 WIiQH ll imm 1w x l x a Cumid r functiun Y z lt x L WSEI k Evaluam C I f 3 xa4 WEE1f Fu kbs vi a a a 74 H5 4 LIL FL W 39p Limits at in nity Nmmzi n fths fun i values appmach a real numb r L as i gcr a eg with hmmdi than WE wrim Jim I L 3493 1mg mn i V il x p pmach a real numbEr as xquot decreasas withuuxt hmmd WEI 1 write Hm I f Hm f L 3 than the Ein3yzi is a rightward hmimm l i I 39 If Kim M whet11h li yM isa e ward h rimmml HEWWWW the graph i5 given Bh k the behaving 0f the giwn mmim as 3 gt m w as I Er arzya L4quot Ftfo EL 3 WPMIEME 22 Winn 13W mclim is d d a ibn uj Himm Hm Jr gt5 512quotquot 9 M Mm W I m 46 17 Mam11mg rquot at a ixrxl Hm AT W a 1 r ay r 4 1 11mm pic 1E 1 EWBZJ w A 23

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