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Unformatted text preview: Math 241 — Exam 1 — 2PM V1
September 25, 2008 50 points possible 1. 10 No hats or dark sunglasses. All hats are to be removed. 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 off 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 time—piece. N0 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? pages. Be sure to print your proper name clearly and then write down the title of the dis cussion section (Le. BD7) 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, close the 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. Good luck. You have ﬁfty minutes to complete the exam. 1. (5pts) Find the volume of the parallelepiped spanned by 3i + j — k, —i — j and j + k. ; M Pg",O/\,m'w[wz~l
ﬁwezddxf) "\\K (M .é>'\
O\\ 2. (Spts) Find an equation of the plane formed by the points A(—2, 0, 5), B(4, ~1, O) and ’21:; ﬁnd/(A '/’(>103<\ "Uﬂf‘ltbqﬁ
~21 [;\\\\B" (’930\C\ : (€)1I*4\ 3 3. Consider the equation y : —Za: + 6. (a) (4pts) Explain What this equation describes in R2 and ﬁnd a parametric equation that deﬁnes the same set of points. A \\,~a, g? r: 72,: “:7 V; W Vat/(Jr /0»(O\ 0‘“ )M‘ﬂ' Qm: [0‘ +«é Mfg t/ (b) (2pts) Explain What the equation y = —3x + 6 deﬁnes in R3. Brieﬂy explain your answer. A w, E— x + \/ + 02: C: L} i a
ﬂaw “/ «1an m; {g/L} ,' \) D\, 4. Let A(3,1,4) and 1(t) = (25, —2t, 223) for all t.
(a) (3pts) Sketch both A and l and sketch the vector that describes the distance from the pointtol. (b) (6pts) Compute the distance between the point an 1. Qeoﬂjjé A‘(;\\)q '3 :7: C’s/9s“ . . y 33
5. C d th f t F , = , , _
on81 er e unc ion (:3 y) (x2 _y2 $2_y2 Macy) (a) (2pts) This function is a mapping from R” to Rm. Determine m and n. (b) (4pts) Find and sketch the domain of this function. Y WA F W: Hlfr\:/\7é+>4 MAY; (Zpts Where is this function continuous? Brieﬂy explain. ) ) i If‘ Vk (LEA/WV), ’
a WW») Since ’9‘ @ML [empower D
A w?083%on «Quirk 00m in [9( (\j (c A wﬁ‘AWS 01*. HEN” AOWV‘ ) [an “ll/(64"; DA % (WPSQA ADA/WA 6. (a) (3pts) State the polar—to—Cartesian Change of variables transformation. y: (“sine (b) (4pm) SketCh the image Of the region '9 Z 0 S r s 3 under this mapping.
zﬂr‘g\’\f“£\\ = (rcosjé )rsm w ’93
‘* (WEN/m )z>,ew;§~ m \ W? @W m \wa—glmce‘ (5M; 3/65 ’1];
Lt. (o,o\ 7. Consider the surface 2 = :62 + y2  9 in R3. (a) (4pts) Sketch the surface described by this equation. A (b) (3pts) Consider the solid formed by the region trapped between the surface and the cry—plane. Describe the solid using inequalities in Cartesian coordinates. ast2>uhm sayﬁsq (c) (3pts) Describe the region using inequalities in cylindrical coordinates.
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This note was uploaded on 02/07/2010 for the course MATH 241 taught by Professor Any during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 Any
 Math, Calculus

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