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M138.W09.TT2.Info

# M138.W09.TT2.Info - MATH 138 INFORMATION FOR TERM TEST 2...

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Unformatted text preview: MATH 138 INFORMATION FOR TERM TEST 2 Winter 2009 ______________________________————————————— TEST 2 will be held IVIonday — March 23 — 7:00-8:45 p.m. (see locations below) NOTE: Term Test 2 will cover problems 6-11 of Assignment 5, (curves in R2), plus all of Assignments 6 & T. & 8 (except for #6.? on Assignment 8). Here’s a list of what you need to know. TO HELP You REVIEW: 0 VECTOR FUNCTIONS: Thinking of x = F(t) = (T(t),y(t)) as a curve in R2, you will need to be able to either eliminate t to get an equation in :L' and y, OR, (ll) sketch component graphs or speciﬁc points and tangents, and combine that information in order to sketch the curve in R2 and assign a direction for increasing 1. Interpreting x = F(t) as the path of a particle moving in R2, know how to ﬁnd its velocity v and acceleration a, and ﬁnd the distance travelled (i.e., how to develop an integral for arc length L, starting from the element AL, as a Rieman integral, or as the integral of the speed of the particle). Be able to find the vector equation of the tangent line to x = F(t) at t = to. and interpret it as the linear approximation £,o(t) to F(t) near it = to, and as the line followed if the particle leaves its path at to. o SEQUENCES: Know the formal deﬁnition of lim l‘" = p; the deﬁnition Of ’monotone’; the state- _—— TI—‘m merits of the limit theorems (LSR, LPR, LQR, LCR), and of the I\I‘Ionot0nic Sequence Theorem. Finding the limit of a sequence using the definition is an essential skill (See Examples 1-5, pages 60—64 of Course Notes), also using Induction and the Monotonic Sequence Theorem (Exs. 1-2. pages 73-75), or using Limit Theorems. You can also use the idea that lim f (n) = 1lingo f for n—'OO , _ _ In n . 111T _ _ continuous f (e.g. hm ——2- = lim Know the limits on p. 68 of Course Notes. 11—00 71, 32—900 :1; . i ‘ ' o LIMIT OF A FUNCTION: Know the formal deﬁnition -(5 — 6) of hm f(:r) = L, and how to use 17—“) this deﬁnition to prove a limit. 0 SERIES: Know the definition of Sn, convergence, divergence, absolute convergence, conditional convergence, and the statement of all theorems (CST, n‘h‘ TT, CT, LCT, IT, ACT, AST, RT) and any corollaries. [Page 2 herein provides a summary for you to complete. as an aid to learning 1 these] You may use WITHOUT PROOF that 2 E converges for p > 1. and GST. ALWAYS check that nlim |a.,,| = 0, sinCe otherwise Zen diverges. The key to series is to do LOTS of #00 examples, so you can learn what test is likely to work. Suggestion: Read page 3 attached, and text p721, and then try text page 722 — #1, 3, 5, 7-15, 17—29. TEST ROOMS: You M T 0 To THE ORRECT - OM — THERE ARE NO EXTRA SEATS! (Last Names) I (Last N E117 MC 1085 (A-Lin) 4020 (M) 001 P. Roh 2017 (Lin-S) 005 1). W'olczuk MC 4021 0'er 2054 (Tm MC 4041 (R:V\»ill) 4042 (iv - (A-Ko) , ( 002 J. Sham 2035 (Ker-Shiv) L. Wang 112 (Li—Tim) (ShO-Z) (Tran-Z) B. Marshman 007 211 (M—Z) RCH 301 004 M. La Croix 302 (L—T) M. Scott RCH 306 (A-Z) 307 STJ 2009. 3014 (TBA) | I). Zhou RCH 305 (A-Z) MﬁTH V69: Summagy cg Semes 0F COMSTAQTS 2Q“, Deghnih'ons a . 4. “Tch 90.:1’ﬂhu95wm 5,4 :8 m wow “Evan L5 2. an is o. cmwwgem‘k wine {g '5. Za“ {s o. AWQM" mm ig ;. 4. Zn“ is a. %e.om€\.n(c. WILD» 1% Li: m 8mm 5. A“ mammary“ mm; mm 8mm 4,. Zen Como-QO O—bSOW Kg '1 20.“ mengm CWOL‘LTL‘O'Wa—Qilj (8 Weorems 1. GST CoroHoxj: ’2. 'n‘kTT a. CT 4». IT QoroHOmy: 5. AST CoroHom): 6:. ACT 1. RT MATH \38 - 5mm Swami Cctd.) P°'°AQB*3 Z Decide what Test To wse '. mu... MM. Co «no Ame. um...» EdoMJ Wane. Acme MM To 99.06% 1. We kmow Z—‘ﬁ? (Leno. Src'LF>‘ sundown/mam 841 95. l. 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