Sample Midterm 3 key

Sample Midterm 3 key - SAMPLE Math 16C Sec 1 (Malkin) Name:...

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Unformatted text preview: SAMPLE Math 16C Sec 1 (Malkin) Name: , Mid-term exam 3 (Sample) Student ID: Mon Dec 1 2008 Signature: ‘ DO NOT TURN OVER THIS PAGE UNTIL INSTRUCTED TO DO SO! Write your name, student ID, and signature NOW! NO NOTES, CALCULATORS, OR BOOKS ARE ALLOWED. NO ASSISTANCE FROM CLASSMATES IS ALLOWED. Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. Be organized and neat, and use notation appropriately. You will be graded on the prOper use of derivative and integral notation. Put units on answers where appropriate. Please write legiblyH ‘ - 20 10 1 _ l- )— l—- l-- _l Page 1 of 6 l l l l l SAMPLE 1. (a) Determine the nth term (starting with n = 1) of each of the following sequences: 1. (5 points) 4, 7, 10, 13, 16, 19,22,25, Qw“3fl+\ ii. (5 points) 1, 2, 6, 24, 120, 720, 5040, ahtni - 2 4 8 16 32 64 128 111. pomts) —I,§,—'2—7,a,—fi,2—16‘,—m,uu n (21‘ an: ("‘5 ’33:“ (b) (5 points) Determine whether the sequence an 2 gnu—fig converges or diverges. If it converges, What does it converge to? t 1... 09 fl YV‘N“ W haw M 3. :41 f 2i Y\'¥V\ 2 , mam \ - Q) My 5&7bwmce LUMLKFjGA cmci Cami/£664 “he 1—- Page 2 of 6 SAMPLE (a) Determine Whether each series conver ges or diverges. You must justify your answer and state which test you are using. 00 2[ Yb! So am Om -: \n-Soo new i. (5 points) 2:; “vx \1 ’— } CL w , I W Jmééédtireéfl (b) (5 points) Find the sum of the series End) (3% + 3. l“ \ v\ “ LL )5 CL (jflwfliflt 86KB ' bhx‘ffi i‘: ’L>\ HMS QM jimeiric Ere/Lake R 00 ‘ .Ovm x Zn=0{ “\~ "7;: L A“ U\k\‘ n L: =§it>VEr3 fiLMQ—E—fl WWW 9% <\ $3??? , . 3nd? "Vow mm M, M t a» #0. {y W M Jam #55 2%»)- v . (b {h 05 : + :3 A10 “‘0 a)“ .I °° ...., 3., fl—gfifiszgé “23M avarice- HZO 0°. 3‘? g 57. Zlhw?) 1.: :25. “0 ":LZ: SAMPLE 3. Find the radius of convergence and the interval of convergence of the following power series. You do NOT need to say What happens at the end points of the interval. (a) (15 points) 22°21 (x _ 1)n' Midwi- ‘ HM“ I M , “i {gigs (Anon (Xvi 7 (in n _ \ “Lf : Jim i ’ 0‘ "Oi : jam i3 imam“) U" )3 O ‘ vvwo g, Hie moth» Muir—ecch (:3 m fi/MQ Mil wok/m»? of cm “576%? 4c I"! (~09 00). {P500 vx 1—. ) M 5 H . E,“- ‘n (w) w 4 / a ’7” )LM : i ' r)— “a; \\ N“ 5 [ \i/h V < l \1+\\<§ (:3 A ()u/\ (g (I) L (1411‘ Page 4 of 6 SAMPLE \ 4. (a) (10 points) Find the Maclaurin series for f = cos(m) by using the fact that = 2:0 (§;i)1")!$2n+1 and %(Sin(w) : cosh»- LL 9 (~ DA hm) : (th (FUNK) f )L K “to (Lun . 00 ($9 V\ , 1i E'DK LwH («0 A, MM) 1’ (M (amid) : ZO/wm doll - h:0 Y\~—/O ‘ 00 V\ : Z a: \ (ix/w 3L1“ ‘va “31 W70 (1“ 3 M QM! : Ow). & V (b) (10 points) Approximate the definite integral fol e“$2dx using the 4th degree Taylor POIynomial for 6"”52 centered at O. Hint: 6‘?” = 20° (-1)" 2n n=0 n! SC . LEA“ Mame/toga @obmmiod :. 1 — 76 Ar 2%,. \ K V L l (L X + 3“ dine 5“ KOQJM‘A LP 3 Page 5 of 6 SAMPLE 5. (10 points) Suppose that a rubber ball, when dropped on a flat concrete surface, rebounds 90 percent of the distance it falls. Find the total vertical distance, both up and down, traveled by the ball if it is dropped from a height of 10 feet onto a flat concrete surface and allowed to bounce up and down freely. u vml\\ (a) Find the total vertical distance, both up and down, traveled by the ball hitting the ground for the nth time? (b) Find the total vertical distance, both up and down, traveled by the ball if it is allowed to keep bouncing forever (Le. n —> 00)? 0“ t \0 ml (1L 4m MM 0 ~— qs : \O wmxlo drown 0% = lOt Log no i Mfitxmi 1.x 09m. D" I k S0) Q“: fl [S QM h:O (ilx‘ramu headed up amid W W“ \iwmoe ““ t it w amt: imam 2mm 40 Vvsov V‘f’c’o kw 1C) 90 \L . w C 2 realm ~\O : \voa ‘0 “’0 L9 y W Wflc 86W“ '- O‘kqgjfl’. ant), v“: M Z \ END OF EXAM Page 6 of 6 ...
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Sample Midterm 3 key - SAMPLE Math 16C Sec 1 (Malkin) Name:...

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