math161 s07 midterm2 - Math 161 Midterm 2 Name\5 Date March...

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Unformatted text preview: Math 161 Midterm 2 Name: \5 - . Date: March 2, 2007 Instructor: Dr. Paul Choboter Time limit: 50 minutes Read all questions carefully, and show all your work neatly. Calculators, books and notes are not permitted. Good luck! Question Score Points possible V 1. Find the derivative of f{m) : 3:32 e 51“ + 7’ using the definition of the derivative. (In this question only the differentiation formulas earn you no points. In all the other questions on this midterm you may and should use differentiation formulas.) £00 3x2 “EM—1 5? (K3: M“ 3 mm: - 5 LX+h3 :1 “"sz bot—U h—vo .Wm—m ”gun-IF' -'—‘ Q 0‘3 £190 X+bxh*éhl%"5hfl*%flfi V -_ 1 V 2. Find the derivative of each function. (3 pts) (a ) f(:c)= —3:r:4 +%+1 .7 my} $00—— .gx4+2:x r” ”s W): -—m3~x 7» / r : .— 9— 3 -—- ___\__ H (x) \ wk ,7 "fr—X3 J (3 pts) Lb) f(:c) ;. $13283 ,5 1 - ‘ , iJF’QO= fie“ 5% l’f/ $111 .I‘ 5f" 2?? o\ x?) 7 C 3 -;——-—t::) a); MW ‘3 ii Cx)‘ ~ L (”2) ELK" 5X :jgllcosw j (3pts)(c)f(m)=(1+$3)1/3 # (3 PtS) (C ) HI )= 7“” ‘\ (¥)_ fl COSXX Coo mm W $2 (03“) ) {T/GC) %7 7mm“ (“00‘ D 5% K: _W_ £766 QM 1(0306‘) - — _ V f“ L: W D QODOM x3 n07 cost“) ”— 2 dy V (5 pts) 3. (a) any“ +332 y: a: + By Findd — in terms of H: and y. fi CX%4+X1®: QC+3d\j)&( x3w +LE§LX+X€1XUJ ggxx :\+3%& x4l5a%*\5+‘*ai afi-‘Wfi 5/ x‘bfig %% + X2%%—*3%&14—LA1X dJ (5 pts) (b) Assume that :r and y are differentiable functions of it. Find —T— when 3:2 +1312 3 25 dt d '2 7: [’1 23C: Mflaffi 2K% +2kjgi$zo d M M3? —. "”7:— 5 _,_ d 0C a a? "' :%”(“13 V— : (—0—— 3% ($1 ——57: V (4 pts) 4. (21) Find an equation of the tangent line to y : I + \/:1_: at :1: 2 4. \j I» (a \5 2‘. 7Q 4r \IX \5‘; 4+r: 4¥11bflmmy€hml q \jmflx L \Lfiflo 2%;(x 4 Us \fl‘:\+.\ix 1 ........ _.._._.——- ______ __ — n. \jf—l 1W ' \ __ .L. h m 1 ("a '; \ + 2W —' ‘4 k 4 7 3;) 49! 04 O (3 pts} (b) Find the 10th derivative of flat ) * eT —/2€6/+§z2+)0 ,.»-—" i We) : eff i (3 pts) ((3) A particle has position (or displacement) given by 5(t) = t2 7 61: + 11, Where t is in seconds. At what instant does the particle have a velocity of zero? SCOL’Clubt +-\\ s’GO=v-— Zt-lo 3 O: 2t*lo Q2 3 2t JC 1 3 '1' r H»; 5. Let y x 51:4 — 4:33 2 m3(x — 4). The first and second derivatives are 3," 2 42:3 w12332 = 4332(2: — 3), and y”212:c2 — 24a: : 12$(sc r 2). {2 pts) (a) What are the :r—coordinates of all the critical points of the function? \5': a”?— (x45) 0 = ‘lxz o N... X (3 pts) (b) For What values of 3: is the curve increasing? For what values of :13 is the curve decreasing? '2— a 03 l : 4V (IS—‘73) b) (—0 z 4002" L4“ :3) V '- 4 (A) 1 "" Us A of} ___.._ -» — ~- ~ +++ [5'03 ”' 4L01(\'®= 9?: X q '00) ~— 4100)" (lo-'3} Wan "100 ' #l " (2 pts) (c) At each local maximum or minimum point, state whether it is a local maximum or Ininiinun1_,_____ and State its; (33d 13319314) ( was" a locdl 'm\mh\(iih gL’D 7. 11(4) = -17 qum “YEW 3 WWW... __ __ _ O, ,. v3 \3 mcr‘eOtthWJFzSFWC%#§D decrEQSmci tor (-00. ’5 ‘V CL (3 pts) ((1) For what values of m is the curve concave up and for What values of a: is it concave down? Lj H ____ \ZX (Xvi) Lj "(\) -_ \2L\)(\-Z) ; ”ll o 2 max ~73 (,3 "(—0 : lat—Devwao 3 o 1 0.x 0 : x "7— g ”(m : ammo-2): + K; x=2 w ,, maeup Arm—Jr ~ ~ —~- HM W on was?) 0 and comm down on UN 2 .--—«~—-—h_.__, ...
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