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by: Julia Tang

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# Study Guide Mid Term 3 MATH 2924 - 010

Marketplace > University of Oklahoma > Math > MATH 2924 - 010 > Study Guide Mid Term 3
Julia Tang
OU
GPA 4.0
Differential and Integral Calculus II

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Over the entire Chapter 11 of the Stewart Calculus book 7e. - Sequences - Series tests
COURSE
Differential and Integral Calculus II
PROF.
TYPE
Study Guide
PAGES
7
WORDS
KARMA
50 ?

## Popular in Math

This 7 page Study Guide was uploaded by Julia Tang on Monday November 16, 2015. The Study Guide belongs to MATH 2924 - 010 at University of Oklahoma taught by Brady in Summer 2015. Since its upload, it has received 35 views. For similar materials see Differential and Integral Calculus II in Math at University of Oklahoma.

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Date Created: 11/16/15
10 Some results about series Geometric Series quot 1 i When r lt 1 converges When r lt 1 it converges to the sum 1T OO n ar Test for Divergence If 23021 an converges then limnnoo an 2 0 Integral Test For f continuous on 1 00 positive and decreasing to 0 the series 2201 f converges if and only if the improper integral floo f xda converges Comparison Tests Direct comparison test compares series of positive terms term by term Limit comparison test compares series of positive terms 2201 an and 221 9 When limgt00 2 L a nite limit not equal to 0 Root Test Let 1imgt00 lanlln L If L lt 1 then 2201 an is absolutely convergent and if L gt 1 then it is divergent Ratio Test lan1 lanl Let 1imgt00 divergent L If L lt 1 then 2201 an is absolutely convergent and if L gt 1 then it is Alternating Series Test If an are positive decreasing to 0 then Zf1 1n1an is convergent Moreover the nth partial sum is Within an1 of the sum of the Whole series Power series Ratio test is useful for computing the radius of convergence of a power series 2200 cna aquot Taylor and Maclaurin Series Taylor series for f centered about a is given by oquot f n a n 93 aquot n0 Maclaurin series for f is the Taylor series for f centered about 0 Remainder Estimate Taylor s inequality states that if f quot1a S M on the interval a d a d then Mlx an1 fw Tnltxgt 7H 1 on the interval a d a d Here Tna is the degree n Taylor polynomial approximation to f Wvl bwdc SM m39 0 s WM M notwch mourn 3 I a a zaq N39mhwquot s otva 333z 33 his 3 W 3 u r 31 lt23 1vg A44 4 VH4 3quot 3 4 5quot an x mm g amzt m t a i i 5 3quotLn r r B 3 q 39 5w E Iwg g a 5 33993 301J39ZGIn5 L3 iwsnf lo b l 12 FM Jr rm an rpm 94We 3 at 49 w quot 3f 395 916 5m S 2 32 J Squot 16 7gquot 3w 163 1quot w h 9mm AWM QJ O T am v0 39 9 C IYM39 C4 7quotquot V WUquotUquotUquotUVU39UquotUU39U39U39U39U39U39U39UUUUU quotquotquot W MW 0 Rwymm 24W 61 hi us kw WWW Jaw bvs W Mthmsr an39I in au v fn gt3 tautL Wm B W of 7 rvcou lwuy KymLg EM I39LF US l57r w An V v v39Lquot nH Hfquot q y39M39 Mrs n1 mam m vA Swlvwwu 227w L w Qn YL as mam t w MMW WMS 3n as aw h Lmj n mqu 1 Ww n Irw 3n l 3 0an own quotm solWoW 02 864M 734 MM L UV 393quot 1 analMQnL39iwla ls w zoo N n 39 vvyvvvvvquotquotquotquotquotquotquoti I f 1AM PM fL sL CV 31quot mm m u 2m MW W AM qwaL nW WM w W Ygto 0 W 3m Mums law M IL Lamasum Muse W wova WM Guava 9amp n4 W 9113 V39WLM M W S M NW M if NgtPJ T M Mgtn4 nghqh00 iawpi A WVW 2 I0 If quot bis LOVi Sk39cul f39 W 2 fur ss 39 i T 39 i r w 1 7 um M9quot I 1 h J P y c w g 77 39 63W TWM f39 5 VW cwn fvr nn UM 3 3 UM ta L M GMBW L 90 10 an LA meow f zo39mmquna o RM HMH new WM W J3 39 AM L l39a gla L vx v MI Mquot n Vm MI HM 41 z quot0 r 1 01y En quot min 4 I 39 i L 2 3 4 gpim my i L 39 l 7 I 39 i L Iquot O Ffz fw 1 r 1 d g Far a gEt gjy jg 71 39 um 39 w gt 39 3 a y 1 quot I frAlf39 H W Mi 1 Miquot 4 39n n 3 a h 30 m 39 VHI u1 T 39 ijl k I I v 39 u v 395 c n Pk a v H u I C 91be n 90 M 125 mem 4 w wsrs h n 39 A WM 2quot chm 4130 W n MW MW 4 0 AM w n vam Mm QW L W 144 Wow us wwh a A L W gym 39f Hquot 3 f A 06039 14m OM va AM 6Wl lqV zm Mgw L phy 5WLDZO n W 7 M l ole An N A A A I lWLT3 H 9WMH JV1 W Dshm SCHS quot H Ms K Wu Wus39 2 L a 930 h Lonv 12gt ON y 392 f EQVMM Earquot P WWWIL W Lonv V DIV Yz 3 f SIMLULV H vaMu or qcuwwhnb W 140v LIMA MM Wmsm Mk 4 323 Uni0 M M or D W S39 i Dquotquot b w 1L4 bu W 64 Sum Tlsr39 Poss ou 9 Ram 02 mam 1 quot aquot 5 m cf Um Hum Loot DH 6 zmz ccm vow J39 fw our 3mmfo Rs dd39ttiouucb c e 3 Vquot w c j ffquot 17 sawv 0 5 V1405 quot quot9 quot39O U39 m 03 25 JAM1 WI 99 waf Low39t f 543M va km 47 v 91 8 39 m 39 5mgquot a u quot V 033 i Z MRP Ll 1 n wi39mgdmng i Wm z u o 0 o a o 6 w a 31311

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