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Unformatted text preview: Name: Puke Math 241 — Exam 2 — 9AM V1
March 15, 2010' Section Registered In: __________ 50 points possible
1. No hats or dark sunglasses. All hats are to be removed. 2., All book bags are to be closed and placed in a way that makes them inaccessible. Do not reach into your bag for anything during the exam. If you need extra pencils, pull them out now. . No cell phones. Turn them oil now. If you are seen with a cell phone in hand during the exam, it will be construed as cheating and you will be asked to leave. This includes using it as a timepiece. . No music systems — IPODS, MP3 players, etc. — or calculators; same rules as with cell phones. . If you have a question, raise your hand and a proctor will come to you. Once you stand up, you are done with the exam. If you have to use the facilities, do so now. You will not be permitted to leave the room and return during the exam. . Every exam is worth a total of 50 points. Check to see that you have all of the pages. Including the cover sheet, each exam has 8 pages. . Be sure to print your proper name clearly and then write down the title of the dis— cussion section (Le. AD?) for which you are registered. . If you ﬁnish early, quietly and respectfully get up and hand in your exam. You need to show your student ID when you hand in the exam. (Drivers license, passport, etc. will work also.) No exam will be accepted without ID. . When time is'up, you will be instructed to put down your writing utensil, closethe exam and remain seated. Anyone seen continuing to write after this announcement
will have their exam marked and lose all points on the page they are writing on. We will come and collect the exams from you. Have your ID ready. 10. Good luck. You have ﬁfty minutes to complete the exam. 1.
(a) (3pts) State'the spherical to Cartesian change of variables. X: : /3§1AA)C086
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(a) (apts) Find a parametrization of the curve c at the intersection of the surfaces xz—y2=z1anda:2+y2=4inR3. 3511924 ":3 le‘l Ksﬂcose ,YTale/Lér . a  a 3 ~ A 9 <9. 1
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7 %{e\ 1 4(0336 ”'Lkinﬂgé} 4“} NW: (Olaea, alone, 4mg; #4935 + \\ )
OE 6,4037. (b) (4pts) Set up, but do not evaluate an integral the calculates the length of the curve of intersection. Hag: 5— [rolgrné, (96056 J “ %@se$me __ ngnezose\ gm : Q limit an; 44cm? 46. 3. (5pts) The velocity of a. particle is given by v(t) := (8t, 5 — 8 sin 273). Where is the particie located at t = 3 if r(0) = (0,10). . ((3% 3’— [7%4+Y¢>\ 7': [O:\O\ Mag %:0} Yogé.
FHA: ;[4J(9) qré+ 4(08&“é+[9\ (‘(%\ r: CﬁQ1§I+4105/L\\  L37 \AAA [(MAVLUV. 4.
(a) (2pts) State the conclusion of Clairaut’b'l‘ eorem. Xi .2 \Q
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(b) (3pts) Compgte fmyz for f($, y, z) := $3111 (yz) + tan (2 + 2—1 ) CM «Cé (igmmxx J E Is (‘9 $_$—
“4/“9 "RN“; 5‘ £7709: ‘ Qim‘oéiz %%Co${\f2\ "‘ 0 .
£7K{%4\%\2: %603(7%\ 5. Suppose that you have the following information concerning a differentiable function f:
f(2, 3) = 12, f(1.98, 3) = 12.1 and f(2, 3.01) = 12.2. (a) (3pts) Use the information to estimate the partial derivatives of f at (2,) 3) C oar» all __ 19.431 ’10 ._—. 4* ,—~ 5K Q 193 “/95 QL)‘%\ Xi :1 l9"l91> :“go? ”IQ/,1} 1. 0'10 157 g .. gm 1,01 l/w
(b) (413133) Find an approximate equation for the plane tangent to the graph of f at (2, 3, 12). )1) wa/xra\ 4190 (X~%\ (c) (3pts) Find an estimate for f(1. 98 2. 98)
a 15 Q1 11.14111» e019 1 6. Let f (5:,y) be a scalarfunction of two variables. (a) (Spins) Deﬁne what it means for f to be a 01 function. Qwh an; Qiexh M (onjrwhmx {mfg
MA. (b) (5pts) Let a: := 8 +1: and y := 3 — it. Show that for any 01 function ﬂat, 3;),
n6f_(n)i(a_f. 2
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58 37k 58 7‘ e3 M: “FEC \ 7. (7pts) A bug located at (3,9,4) begins ﬂying at unit speed (1 meter per second) in a
straight line toward (5, 7, 3). At what rate is the bug’s temperature changing if the temper— ...
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 Fall '08
 Kim
 Math, Calculus

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