Math 32B‚ Lecture 2 Fall 2010 Practice Problems for Final (sections 17.6-17.9 1. (0 points) (a) Let C be a simple closed piecewise-smooth space curve which lies entirely in a plane‚ and suppose that the plane has upward-pointing unit normal vector given by n = ai + bj + ck. Show that the area of the portion of the plane enclosed by C is 1 2 C (bz − cy) dx + (cx − az) dy + (ay − bx) dz. (b) Let C be a simple closed smooth curve in the plane 2x + 2y + z = 2‚ oriented counter-clockwise
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demanding when I became a high school student. It was quite a transition period as much as I can recall. Mathematics that was taught to us became more complex and was somehow much more difficult than what I was doing in primary school. High school math was presented as something straight forward. Our teachers during that time presented examples in class and gave the homework without further explanation. I knew I had to work hard and concentrate in order to get decent grades. The problems involved
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1 2. Establish each of the following for all n ≥ 1 by the Principle of Mathematical Induction. Solution a) S(n): ==‚ S(1): = = =1‚ So S(1) is true. Assume S(k): = Consider S(k+1) = = +=-1+= -1. Hence‚ it follows that S(k)⇒S(k + 1) is true for all n ∈ Z+ by the Principle of Mathematical Induction. b) S( n) for n=1‚ = 2 = 2+(1-1). So S(1) is true. Inductive Step: assume S(k)is true‚ for some (particular) k ∈ Z+—that is‚ assume that =2+(k-1). For n=k+1‚ = + (k+1) = 2+ (k-1)+(k+1)=
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Pedram Ghodrati Math Why do we have to learn algebra? Math is an academic subject which many students struggle to master. I remember when I was in high school‚ I always had a hard time understanding math. In senior year I almost dropped out of school because of the difficulty of high levels of math classes. I just read an article called‚ “Is Algebra Necessary?” by Andrew Hacker‚ an American political scientist and public intellectual. He is currently Professor Emeritus in the Department of Political
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During perusal‚ write on the blank paper provided 3:00 Hours Mark Russell This examination paper has 18 pages (not including the title page) and is printed Double-Sided THIS EXAMINATION PAPER MUST NOT BE REMOVED FROM THE EXAMINATION ROOM Exam Type: Closed Book - Specified materials permitted Examiner’s use ONLY Question Mark Permitted Materials: Calculator Yes- Any calculator permitted- unrestricted Dictionary Yes- Any unmarked paper dictionary is permitted Other- No
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Running head: PSYCHOSOCIAL STAGE OF DEVELOPMENT PAPER Psychosocial Stage of Development Paper Tristam Craig PSY 504 Oct 03‚ 2010 Elisa Doebler-Irvine Psychosocial Stage of Development Paper The theory of Erik Erikson is that the early childhood years are very important stages of the development of the personality of an individual. This theory followed many of the principals of theories developed by Sigmund Freud‚ in relation to the id‚ ego and superego and the theory of sexuality
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Past and Current Trends Paper Tammy Poe PSY 425 August 6‚ 2012 Professor Mc Keon Past and Current Trends Paper Substance abuse in the United States has changed over the years‚ and comes in many forms‚ such as prescription pills‚ non-prescription pills‚ powder cocaine‚ crack-cocaine‚ meth‚ heroin‚ marijuana‚ tobacco‚ and alcohol. Today‚ there are advertisements sending out messages about how drugs can harm an individual‚ their families‚ and their future. There are people who admit to doing
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IB DIPLOMA PROGRAMME PROGRAMME DU DIPLÔME DU BI PROGRAMA DEL DIPLOMA DEL BI M07/2/ANFRE/SP1/FRE/TZ0/XX/Q+ 22072804 FRENCH AB INITIO – STANDARD LEVEL – PAPER 1 FRANçAiS AB INITIO – NiVEAU MoyEN – éPREUVE 1 FRANCéS AB INITIO – NiVEL MEDio – PRUEBA 1 Wednesday 23 May 2007 (morning) Mercredi 23 mai 2007 (matin) Miércoles 23 de mayo de 2007 (mañana) 1 h 30 m 0 Candidate session number Numéro de session du candidat Número de convocatoria del alumno 0 QUESTION AND ANSWER BOOKLET – INSTRUCTIONS
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Paper Reference(s) 6667 Edexcel GCE Further Pure Mathematics FP1 Advanced Level Specimen Paper Time: 1 hour 30 minutes Materials required for examination Answer Book (AB16) Graph Paper (ASG2) Mathematical Formulae (Lilac) Items included with question papers Nil Candidates may use any calculator EXCEPT those with the facility for symbolic algebra‚ differentiation and/or integration. Thus candidates may NOT use calculators such as the Texas Instruments TI-89‚ TI-92‚ Casio CFX-9970G‚ Hewlett
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Yr 10 Mathematics Assignment LCR Maths By Adonis Chigeza Understanding and Fluency Tasks Task A 1. y = 1.2? + 2.57 2. Interpolation: y = -3.43 Extrapolation: y = -8.23 Task B a) The equation for the path of the ball is h = -0.1t^2 + 0.9t + 1 (h = height‚ t = time) b) The vertical height of the ball after 2. seconds2.664m c) The maximum height reached by the ball is 3.025m d) The time of with the ball is at maximum height of 3.025 is 4.5 seconds e) The total time in which the
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