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Sol-165E2-F2000

# Sol-165E2-F2000 - MA 165 EXAM 2 Fall 2000 Page 1/4 b Page 1...

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Unformatted text preview: MA 165 EXAM 2 Fall 2000 Page 1/4 b . Page 1 / 16 Page .2 I /32_ Page 3 /26 A NAME GEﬁDINg’; I4 E‘Z STUDENT ID “AEGIWON—INSEPRIJGEQR ' Page 4 / 26 RECITATION TIME TOTAL / 100 DIRECTIONS 1 . Write your name, student ID number, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3 and 4. 2. The test has four (4) pages, including this one. . Write-your answers in the boxes provided. . You must show sufﬁcient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes or calculators may be used on this exam. to (16) r 1. Find the derivative of the following functions. (It is not necessary to simplify). (a) y = 6‘59“ cos 3:3 N P C Eli: e—Sx' (d) y = ‘ll + sin2(3:1:) 9124.11.”— dx 2 ‘ 1+si‘n913x) K 355ni3x)ms(?:>q \ll + SimzCsx) MA 165 . EXAM 2 Fall 2000 r Page 2/4 Name: (8) '2. Find 3% by implicit diﬁerention, if .7269 = y 1. + e —-— ,_... at): M ‘ ‘5’ (X e94.) 9L:- :: —- e- 0“ “2r Aw/ 8‘? ..—--' 1“- M 22%- ——---—-~X:M K222» M ta - 2 2 _ . (9) 3. Find anequation of the tangent line tothe ellipse %—+g€ = 1 at the point. (~1,4\/§). - ﬁx 2"} M :0 A q + ’36 M E: - __ ﬂ . de " “l ( 1 ; :dit——4'm'l 1-"‘ : 3—413 :JVE(X+1> 3—45-— ﬁCXM) [f] (9) 4. Evaluate each expression: _ N (a) 003‘1 <2??? 9095:1312 05%éw ® wan-1+» =3 <=> Waviriﬂ‘g 6—9 , -1 ‘ , :3 V tinﬂgzﬁ (6) 5. Find the derivative ofy = :3“. 3 %:x*: “4"” (2) 9.. :MEXQ/nxcg %:BXL”X(X§ Hm”) % i; x Ln 0 h ————— -: 1+ 7? :QXQ x(1+€mx) Am _\3(- 3 "' w ' K 0v ‘ l MA 165 EXAM 2 Fall 2000 Page 3/4 Name: (6) Find the second derivative of h(.'n) = tan—101:2). I L ax __ 2x X :W -— W h“ 1+x“ la—X" h”(><) —..—. (1 +702 - “4"? (1+qu‘ Ron, -qu' +2. (‘3) 0+10t' — -—— (10) 7. The position of a particle is given by the equation 3 = 5 cos 2t. ’1'” (or , Find all values of t in the interval [0,11'] for which ‘ "no"? vain-QM (a) the velocity is 0. «Ina—5x ::-—10 si‘n'zt @ Q):O '. sinafzo —-? she/132W (b) the acceleration is 0. I or: We -=l® 11' 3T!” .. Tl“ 311‘ I: l t' “E ’ A» 4 > a“: 33‘ (10) 8. Gravel is being dumped from a conveyor belt at the rate of 30 ft3 / min and its coarse- ness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high? (V = -_.1;7r'r2h). (D D : saga llama” , L new) D-.—_\« I ﬂaw 42%;; \(-_1 2 .. D 7- 's F“ GU: .- ...3_1w k _..l.n—(_.) h,mdt 04W we. 3 9. “12 V "Bf é! .. Tr" 10qu all ‘Zh When lj:102 '30:.TEL10fﬂL-ll maize _ e . - m“m "7571-;me ,ﬁ—lt/m'.“ m MA 165 EXAM 2 Fall 2000 Page 4/4 ' Name: 1(12) 9. A snowball melts so that its surface area decreases at the rate of 2 cmz/min. How fast is the volume decreasing when the radius is 8 cm? (V = §1rr3, S = 47rr2). Vtvohmﬂ.) W, T‘s‘lwws éﬁt— 25m2/[email protected] Final: a“; mum WEE“?! (its __ ,molv (XV __ L3“. V’QWB‘EQ’) 75"Wts:@ Av_.1 £2 ._% WW v23: KIM—5‘“:de ~2;sneir_ 4£;,}[email protected] 63’ «wail—3;: “1. all 32‘ “CE. “W ﬂz4ﬂ3 ~%ﬁ)=~3© 60/ A969 ' out '5 , a“: Z ‘ (:ng '2 Tl/LL volumlén clement-sin; allude “3114* /M\n 1 , (8) 10. Use a differential (or equivalently a linear approximation) to estimate 36. . Ema §e)+§’(a>(x»m) (23 93; ﬁxwtxng1+419® ,— Let 4mm ,a=ae.. yang? Lat‘ WM? (max wﬁrigﬁous<@ ﬁx Q + ‘(x_36) 1‘ 2% \13334 9:. y+s>i—v§:6(0.4)=§vfﬁ-Gj war-Mm: he: as, C, + A. (eel-3(3):. - L ' 12 ' 72x :Q +_.4;—— : ~ 12,0R W ﬂlzo (6) 11. Find the differential cly if (a) y = tan(3x) CUJ : 648(5):)3 ch dya :- 3 \$486”) 8.x I G) (b) y = msec2m v rib} :: [x 2<\$ux)(mc 7;)"me + uczx‘k cLIy o‘r’ (’5 eecix (9nd:qu + ’1) ix ® ...
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