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Sol-161E2-F2008

Sol-161E2-F2008 - SOLUWOMS MA 16100 Exam II Fall 2008 1 The...

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Unformatted text preview: SOLUWOMS MA 16100 Exam II Fall 2008 1. The graph of y = f (m) is shown below. $0 Pa, PQSVHM. 04M} wggmadrwua L \ ow (X15 0"” a3, :10 _<_ —1 m + 1, ~1 < a: S 0 2. L t = 9 fix) w2+1, O<m$1 2w, 1 < it Find the points at Which f is NOT differentiable. \ \ A.x=0,a:=1,andac=— “i: Ci\ (Ficff/Khfibit @‘i 0 QQ r34 ”0/17““?er B.a:=0anda:=1 5 “\pl 1} O M l . 1) SC My “‘2 W1 MM @gg = 0 and m = —1 r; m- i’ mi Ci (WWW/H bit ”j? X:*‘ $0M" D.a:=1andm=——1 anciwafifi Vi“ 5"" E 33:0 xQWW {a 1-1, Edi” “VHF“ X151“! ’9 m MMWW “vi“ Y" 0 ”Ga M M gran JmQH) (31;: ' (0 (PW) {ii 3: i 34““ ‘ 3’9”“ 7: AW ’FQflgfii’T' _ WV“ “12:23 i iaM ‘ r 2 1 \ bask M €N~>ifi€LCM+ w s; \M (UT/JUL M (NH W‘Of *0 WOX‘OF WW" ”3227"“ ’wx‘i" w 4 LS A waffledwm afi‘ X37: ( mm MA 16100 Exam II Fall 2008 3. At time 0 a ball is thrown directly upward from a platform 10m tall. Its height above the ground after t seconds is s 2 —5t2 + 5t + 10, Where s is in meters. The ball hits the ground after 2 seconds. What is its velocity at impact? Qfé A.0 V/ti": (M; slot +6 B. —5 m/s I __ 3: W 5”“ (2. —1O III/S Vfi) w (ME/Pr? L3 i). l5m/s E ~20 m/s 4. At which point(s) does the curve y = $3 — 651:2 + 1250 + 7 have a horizontal tangent? A. :1: : 0 and w :2 1 £1.)an Ella : @; B.m=1anda:=2 (57‘ C.:c=0and:v=2 Agw~ Z D.1L'=1 «7 2: 3x ~\’L>< +11 E. =2 it ‘ O MA 16100 Exam II 5. If f(:c) = «a? e“, then f’(4) = J, (3 O ‘5: * '6 fr ? «6, Lf : i Li, ”5" Z : a, Li 6. If f(a:) = (1 +Sin233)10, then f’<g—) :- 0) Fall 2008 .w .o .w @ filwfilmoNIHp|© F11 MA 16100 Exam II Fall 2008 7. If g(:z: )2 tan (Wfl 30),) Where f(0 =0 and f (:0) 2, theng’ (0): [SQJE‘W MI ”M (“10% 5% [93(0) WEE: QB E. Cannot be determined MW”? H [A l |._.n V N) [OH-4 + H [to $28 to V <2 (§ 3 mm : gww iZflXEJ—WHZ» age—13:2) K I g 2 ”X39 4m: 1 If; w 31:) Be MA 16100 ExaIn II Fall 2008 3 9. Find an equation for the line tangent to the graph of y— — {fl—J: at the point (e, e 3.) % .w 3741AQJ‘” 75(Ti) ©J=262$—e3 new, -111-“ “WM/«m B. y =2 26% + 63 ~ 3 A7” @3) 1 C. y = 2623: + e ‘ .1 ”2W 9) D. y = ~e2a: + e Ski-J :6: Z 6:4“ a gig :1, 2% _, L E. y = —e% — e 11 W 2‘ W rQe/ , 2 3 .5 g": ZQX’ZE/ “Jrf/ EZQXAQ dy 10. Use implicit differentiation to find 8—y— at the point (1, 2) if m4 —— 31:23] + 312+ 3,13 _ —.7 a: $511M 3, 24L eh i 5 dx > Lhk (mg +2X jfinflgfjflgzéfi Q1 0323"” 9—“ (ll + 2 '%;\ +91% + 1245*“:013. 3 MA 16100 Exam II Fall 2008 11. Let y— — xtana’. Findd dy‘ A. dy da: 2 2 22 x 2222 v» <2 2%) 2:1?“ ”3 (sec 30 tan :8 Ina: + tan :13) d: 2 )gjgm = $133” (seczmlna: + my”) 222 (22122222 22 22 2 g! E fig 2 53”” (sec2 at) Ida: d w {222 2 I if 2 X (Sec @2qu2“ W 2 12. A spherical balloon increases in radius by1 -2— inch per minute. Find the average rate of change of the volume of the balloon (m11n9he53te) when the radius 1ncreases from 2 inches to 4 inches (Volume of sphere: V— — garg’ ). A 2871' inches3 2,2 fl \ ' minute Av , V(2):v(2; 2 2 B. W / WW" Z minute A" t (+ng C 16 inches3 ' 7r minute a , ’33 2222 Li fl 2222 EL E7}: inches3 W 3 TT (4 2: WE: ,L D 3 minute .‘ 7W ‘ L 56—7r inches3 Z E. 3 minute [1ft 2 “‘3“, 2,37 2i (2022: QMQYQ: 2 22 22 2,2,. 1 A2 AV A2 MA 16100 Exam II Fall 2008 13. 60% of a radioactive substance decays in 3 hours. What is the ha1f~life of the sub— stance? M7 A(f\r:: AM) a A.3(ln% A N3}: 0 %fi(@\: M e: ‘( 2‘ W Am 31a »» tfig—gfi * in: N NW, "I“ C. 3( g ) hours W Wt w t In 2 "’9 A06 2:: A03) 6 D.3<1n 3) hours , w {t _ 111% '5‘2‘; Mai :3 We) e e W" ‘g‘ 13.3 (g) hours was.) X: 3%: '3" @Wm; <1? «it» In ’2' 14. Two sides of a triangle are 3 in. and 7 in. and the angle between them is increasing at 0.2 radians per minute. Find the rate at which the area of the triangle is increasing when the angle between the sides is %? le/g inches2 fl 3 9k 9 A T minute WM ‘. $6.” is J. Bill?" B _2_1 inches2 4;?” 5- WC» A 10 minute C. 3% inches2 {20M £13K: WW H;fi 10 minute (if . Q7 21 inches2 20 minute “ , lx/g inches2 WL 9/> E. 20 minute MA 16100 Exam II Fall 2008 15. A 5 foot ladder standing on level ground leans against a vertical wall. The bottom of the ladder is pulled away from the wall at 2 ft / see. How fast is the AREA under the ladder changing When the top of the ladder is 4 feet above the ground? A 25 ftZ/sec Wow; $1.} 2:: .47 ftZ/sec (DH/f .—6 ft2/see Wall 5 foot ladder 3 D. —— ftZ/sec want : {If MM {7: Lf :5 Ground E. —-Z ft2/SGC A all” 2’ chi? +Xfi) A ...
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