Math241_Exam1Solns_9AM_Fall09 - Math 241 — Exam 1 — 9AM...

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Unformatted text preview: Math 241 — Exam 1 — 9AM 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. N 0 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 7 pages. Be sure to print your proper name clearly and then write down the title of the dis- cussion section (i.e. 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, 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. Section Regist red In: ________ .._ 1. Let a = (1/2,1/2,1/2,1/2) and b = (0,~1,0,—1). - (a) (2pts)Determine if either vector is a unit vector. ;: 1 2 2g fl; wt MU J‘HW 4+ ‘7‘ F l ' a if! HM:L;TQ;T :JJs b) (3pts) Determine the angle between these two vectors. ( my) 2 MM (039 {’A.)/a,’é.‘}o\\6 zorma‘x : ([email protected]+O’%;:¢S&me @ (95$ \ C086 2. Consider the two vectors i+ j — 2k and —2i‘+ 3j + k. (a) (2pts) Sketch the parallelogram formed by these two vectors. Q;[l,l}";\ l 5 Aegh (b) (3pts) Find the vector description of all the points that Kelong to the parallelogram. FIEHA: S(l\lrc§\+%(—d,g,\ 9 0599’-l ,oelq (c) (5pts) Find the area of the parallelogram. 0mm (g; 954 ; (m a\ 2: [:71 ~§ §A> 0N5 Xl~c§\%‘,\\ I / 0% (fl:— WW "lac, 3. Consider the line 105) = (2 + 275, —3 +15, 1 — t) for all t and the plane 2:1: — 3y + z = 4. (a) (4pts) Show that the line 1 is parallel to the plane. “ an: (one. :8 +~Ha1 1 ,-t\ we“ W“ Hath, P‘mvmg'g le lg fl:(;l—gll\ (b) (6pts) Find the distance between the line and the plane. (grep a Fowl” onAvla Plawfi, l 3103+§/0\ 9:514 «5:7 Pmmék 4+fi4—l “4 4. Consider the function f (x, y) = 6502412. (a) (Zpts) This function is a mapping from R” to Rm. Determine m and n. Via-v; Mal (Zpts Is this function scalar—valued or vector—valued? Briefly explain. (b) ) SCAM» 3 4L; acififi‘ is a §Calcf. (c) (4pt33 Compute and sketch the level curves of the function f (93, ex”: \4. we xafz mL Movle bf—l :7 X27930 Ala) l; em nélke lksfi‘llami lpemeé v ‘ y — 1 6503’ 5. ConSIder the function F(CL‘, y) = (8111(27 + y), my , :c (a) (3pts) Determine Where this function is continuous. Sm [>€~L\{\ (mtnwwx ' Lfl (mt um \Po mi tawéo C/?»€~y¥m’ vmf . X 8 y JQ‘A Y 71 O (b) (4pts) Evaluate the limit lim (m,y)—>(1»1) k . ,5 M g (4+\ \w \sm 6“) (Jig; (\‘Bg7<,\{\ P ( lifiSaChh A \1 )(%,\{\6 U” fly ) HN\—B (Mk V : /S\n(;\ \\M E e\ awn/j? )(x.j\a(m\ \. 7;) T :; [gm/Q) \\4\/\ EFL“; \{wfl : [Sm(é\\’ \V‘” “1/” )€\ F W "l '2 /S\A{&\\\)€\) 6 (a) (3pts) State the spherical-to—Cartesian change of variables transformation. y": "Psm 49 508-6 \/ f; ?Sin¢ SW6 a1:— PM (b) (3pts) Sketch the region D in p9¢—space defined by ,0 = 2, 0 g 9 g 27r and 0 g 45 S 7r/2. Cb ...
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Math241_Exam1Solns_9AM_Fall09 - Math 241 — Exam 1 — 9AM...

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