Course Hero - We put you ahead of the curve!
You have requested the below document.
Sign up now to view this document for free!
- Title: CryptoHomework5
- Type: Notes
- School: Minnesota
- Course: MATH 2008
- Term: Fall
Coursehero >> Minnesota >> Minnesota >> MATH 2008
Path: Minnesota >> PR >> 2008 Fall, 2008
Path: Minnesota >> PR >> 2008 Fall, 2008
Path: Minnesota >> CCSE >> 09 Fall, 2008
Path: Minnesota >> IMA >> 10 Fall, 2008
Path: Minnesota >> IMA >> 1 Fall, 2008
Path: Minnesota >> SCIENCE >> 09 Fall, 2008
Path: Minnesota >> GANDALF >> 2007 Fall, 2008
Path: Minnesota >> GANDALF >> 2003 Fall, 2008
Path: Minnesota >> GANDALF >> 2000 Fall, 2008
Path: Minnesota >> GANDALF >> 00 Fall, 2008
Path: Minnesota >> GANDALF >> 07 Fall, 2008
Path: Minnesota >> GANDALF >> 06 Fall, 2008
Path: Minnesota >> GANDALF >> 05 Fall, 2008
Path: Minnesota >> GANDALF >> 05 Fall, 2008
Path: Minnesota >> GANDALF >> 06 Fall, 2008
Path: Minnesota >> GANDALF >> 05 Fall, 2008
Path: Minnesota >> GANDALF >> 05 Fall, 2008
Path: Minnesota >> GANDALF >> 05 Fall, 2008
Path: Minnesota >> GANDALF >> 07 Fall, 2008
Path: Minnesota >> P >> 67 Fall, 2008
Path: Minnesota >> WWW-USERS >> 05 Fall, 2008
Path: Minnesota >> GANDALF >> 03 Fall, 2008
Path: Minnesota >> GANDALF >> 2006 Fall, 2008
Path: Minnesota >> GANDALF >> 2003 Fall, 2008
Path: Minnesota >> GANDALF >> 0602 Fall, 2008
Path: Minnesota >> GANDALF >> 99 Fall, 2008
Path: Minnesota >> GANDALF >> 99 Fall, 2008
Path: Minnesota >> GANDALF >> 99 Fall, 2008
Path: Minnesota >> GANDALF >> 99 Fall, 2008
Path: Minnesota >> GANDALF >> 99 Fall, 2008
Path: Minnesota >> GANDALF >> 98 Fall, 2008
Path: Minnesota >> GANDALF >> 98 Fall, 2008
Path: Minnesota >> GANDALF >> 98 Fall, 2008
Path: Minnesota >> GANDALF >> 1998 Fall, 2008
Path: Minnesota >> GANDALF >> 98 Fall, 2008
Path: Minnesota >> GANDALF >> 1999 Fall, 2008
Path: Minnesota >> GANDALF >> 1999 Fall, 2008
Path: Minnesota >> GANDALF >> 1998 Fall, 2008
Path: Minnesota >> GANDALF >> 97 Fall, 2008
Path: Minnesota >> GANDALF >> 1998 Fall, 2008
Path: Minnesota >> GANDALF >> 1997 Fall, 2008
Path: Minnesota >> GANDALF >> 95 Fall, 2008
Path: Minnesota >> GANDALF >> 87 Fall, 2008
Path: Minnesota >> GANDALF >> 3 Fall, 2008
Path: Minnesota >> GANDALF >> 4 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Path: Minnesota >> MATH >> 018 Fall, 2008
Course Hero has millions of student submitted documents similar to the one below including study guides, homework solutions, papers, and exam answer keys.
5248 Math Cryptology and Number Theory: Extra Problems for Homework 5 (1) Compute (n) for the following integers n: 9, 12, 15, 91, 100. (2) Prove that (n) divides (n) for every positive integer n. (3) Suppose n is an odd squarefree number, and write n = p1 p2 pk as a product of distinct primes. Show that n is a Carmichael number exactly if k > 1 and = n 1 mod pi 1 for all 1 i k. (4) Prove that 3 11 17 = 561 is a Carmichael number. You might nd the previous problem helpful. Extra credit: Prove or disprove: There exists a sequence {sn } such that every n=1 positive integer k is equal to sn for exactly one n, and for all n Z>0 , one has s1 + s2 + + sn = 0 modulo n. 1
Find millions of documents here - Study Guides, Homework Solutions, Papers, Exam Answer Keys and more.
Course Hero has millions of course related materials that will enable you to learn better, faster and get an A in all your courses.
Below is a small sample set of documents:
pr2008_01.pdf
Path: Minnesota >> PR >> 2008 Fall, 2008
Description: Computing with Things Small, Wet and Random Marc Riedel Electrical and Computer Engineering / Digital Technology Center University of Minnesota Brians Automated Modular Biochemical Instantiator (BAMBI) Synthetic Biology Positioned as an engineerin...
pr2008_02.pdfPath: Minnesota >> PR >> 2008 Fall, 2008
Description: !\"#$%%\'+(./*0%1.(*+,*2+-1!(%2%*3 *%\"4#\"%4 5676897:; <=6>?*=@B *:>C*D *E<:FG 6? H<I J K LJ M LK N 0(2*HO8>C*+P@:P6@Q J !\"#$%%\'+(./*0%1.(*+,*2+-1!(%2%*3 *%\"4#\"%4 +P@:P6@Q *R*5676897:;...
pr2008_03.pdfPath: Minnesota >> PR >> 2008 Fall, 2008
Description: Computational Synthetic Biology Yiannis N. Kaznessis University of Minnesota Department of Chemical Engineering and Materials Science !\"#\"$%\"&\' ()*+ Gene expression Transcription Translation Gene Regulation Activation Repression Induction Gene ...
CareerUpdateJan09.pdfPath: Minnesota >> CCSE >> 09 Fall, 2008
Description: www.ccse.umn.edu January 2009 Welcome Back to the Spring Semester! IT Job and Internship Fair Tuesday, January 27, 2009 10 a.m.4 p.m. Great Hall, Coffman Memorial Union The IT Job and Internship Fair is an opportunity for IT students to network an...
ID_Mailing_Card.pdfPath: Minnesota >> IMA >> 10 Fall, 2008
Description: Institute for Mathematics and its Applications Surfing with Wavelets Wednesday October 29, 2008 7:00 pm 125 Willey Hall 225 19th Avenue South University of Minnesota Minneapolis IMA Public Lecture Series Wavelets are used in the analysis of sounds ...
RG_Mailing_Card.pdfPath: Minnesota >> IMA >> 1 Fall, 2008
Description: Institute for Mathematics and its Applications IMA Public Lecture Series MATH MATTERS Mathematics Making Sense of Sensors Sensor networks monitor environmental changes in rain forests and are used in nanotechnology and biomedical testing. They are...
science-09-28-07.pdfPath: Minnesota >> SCIENCE >> 09 Fall, 2008
Description: MOBIUS TRANSFORMATIONS REVEALED 2007 VISUALIZATION CHALLENGE Douglas N. Arnold and Jonathan Rogness, University of Minnesota, Minneapolis ANY REAL NUMBER CAN BE PLOTTED ON A LINE THAT RUNS FROM NEGATIVE TO POSITIVE infinity, but throw in an imaginar...
kallie2007.pdfPath: Minnesota >> GANDALF >> 2007 Fall, 2008
Description: Journal of Experimental Psychology: Human Perception and Performance 2007, Vol. 33, No. 1, 183200 Copyright 2007 by the American Psychological Association 0096-1523/07/$12.00 DOI: 10.1037/0096-1523.33.1.183 Variability in Stepping Direction Explain...
SchraterSPIE2003.pdfPath: Minnesota >> GANDALF >> 2003 Fall, 2008
Description: Bayesian data fusion and credit assignment in vision and fMRI data analysis Paul R. Schrater a Departments of Psychology and Computer Science & Engineering, University of Minnesota, N218 Elliott Hall, 75 E. River Rd., Minneapolis, MN, U.S.A. ABSTRAC...
SchraterKerstenIJCV2000.pdfPath: Minnesota >> GANDALF >> 2000 Fall, 2008
Description: International Journal of Computer Vision 40(1), 7391, 2000 c 2000 Kluwer Academic Publishers. Manufactured in The Netherlands. How Optimal Depth Cue Integration Depends on the Task PAUL R. SCHRATER AND DANIEL KERSTEN Department of Psychology, Univer...
SchKer00MIT.pdfPath: Minnesota >> GANDALF >> 00 Fall, 2008
Description: 2 Vision, Psychophysics and Bayes Paul Schrater and Daniel Kersten Introduction Neural information processing research has progressed in two often divergent directions. On the one hand, computational neuroscience has advanced our understanding of t...
IROS07_1136_MS.pdfPath: Minnesota >> GANDALF >> 07 Fall, 2008
Description: CONFIDENTIAL. Limited circulation. For review only. Handling shape and contact location uncertainty in grasping two-dimensional planar objects Vassilios N. Christopoulos and Paul Schrater Abstract This paper addresses the problem of selecting contac...
VeerSchPapa06.pdfPath: Minnesota >> GANDALF >> 06 Fall, 2008
Description: Proceedings of the 2006 IEEE International Conference on Robotics and Automation Orlando, Florida - May 2006 Adaptive Geometric Templates for Feature Matching Harini Veeraraghavan Paul Schrater Nikolaos Papanikolopoulos Department of Computer Scienc...
VeerSchPapa05.pdfPath: Minnesota >> GANDALF >> 05 Fall, 2008
Description: Proceedings of the 13th Mediterranean Conference on Control and Automation Limassol, Cyprus, June 27-29, 2005 WeA06-1 Switching Kalman Filter-Based Approach for Tracking and Event Detection at Trafc Intersections Harini Veeraraghavan Paul Schrater ...
Veeretal05.pdfPath: Minnesota >> GANDALF >> 05 Fall, 2008
Description: Proceedings of the 8th International IEEE Conference on Intelligent Transportation Systems Vienna, Austria, September 13-16, 2005 TC4.2 Driver Activity Monitoring through Supervised and Unsupervised Learning Harini Veeraraghavan Stefan Atev Nathani...
VeerPapaSch06.pdfPath: Minnesota >> GANDALF >> 06 Fall, 2008
Description: Proceedings of the IEEE ITSC 2006 2006 IEEE Intelligent Transportation Systems Conference Toronto, Canada, September 17-20, 2006 WA4.1 Deterministic Sampling-based Switching Kalman Filtering for Vehicle Tracking Harini Veeraraghavan Nikolaos Papani...
Bodoretal05.pdfPath: Minnesota >> GANDALF >> 05 Fall, 2008
Description: Mobile Camera Positioning to Optimize the Observability of Human Activity Recognition Tasks Robert Bodor, Andrew Drenner, Michael Janssen, Paul Schrater, and Nikolaos Papanikolopoulos Department of Computer Science and Engineering University of Minn...
BodorSchPapa05.pdfPath: Minnesota >> GANDALF >> 05 Fall, 2008
Description: Multi-Camera Positioning to Optimize Task Observability Robert Bodor, Paul Schrater, and Nikolaos Papanikolopoulos Department of Computer Science and Engineering University of Minnesota Minneapolis, Minnesota, 55455 {rbodor,schrater,npapas}@cs.umn.ed...
SundarSch05.pdfPath: Minnesota >> GANDALF >> 05 Fall, 2008
Description: Bayesian Modelling of Camera Calibration and Reconstruction Rashmi Sundareswara and Paul R. Schrater Computer Science University of Minnesota Twin Cities, MN 55455 sundares@cs.umn.edu, schrater@umn.edu Abstract Camera calibration methods, whether im...
Ketter07tr.pdfPath: Minnesota >> GANDALF >> 07 Fall, 2008
Description: Detecting and Forecasting Economic Regimes in Automated Exchanges Wolfgang Ketter , John Collins , Maria Gini , Alok Gupta , and Paul Schrater Dept. of Decision and Information Sciences, Rotterdam Sch. of Mgmt., Erasmus University Dept. of Computer...
p67-jensen.pdfPath: Minnesota >> P >> 67 Fall, 2008
Description: Rapid On-line Temporal Sequence Prediction by an Adaptive Agent Steven Jensen, Daniel Boley, Maria Gini, and Paul Schrater Department of Computer Science and Engineering University of Minnesota {sjensen,boley,gini,schrater}@cs.umn.edu ABSTRACT Robus...
aaai05c.pdfPath: Minnesota >> WWW-USERS >> 05 Fall, 2008
Description: Non-stationary Policy Learning in 2-player Zero Sum Games Content Areas: machine learning, Markov decision processes, reinforcement learning Abstract A key challenge in multiagent environments is the construction of agents that are able to learn whi...
SundSchrater03.pdfPath: Minnesota >> GANDALF >> 03 Fall, 2008
Description: Extensible Point Location Algorithm Rashmi Sundareswara and Paul Schrater Department of Computer Science and Engineering University of Minnesota, Twin Cities, USA sundares@cs.umn.edu, schrater@umn.edu Abstract We present a general walk-through point...
yuillekerstenTICs2006.pdfPath: Minnesota >> GANDALF >> 2006 Fall, 2008
Description: Opinion TRENDS in Cognitive Sciences Vol.10 No.7 July 2006 Special Issue: Probabilistic models of cognition Vision as Bayesian inference: analysis by synthesis? Alan Yuille1 and Daniel Kersten2 1 2 Departments of Statistics, UCLA, San Francisco,...
KerstenYuilleApr2003.pdfPath: Minnesota >> GANDALF >> 2003 Fall, 2008
Description: 1 Bayesian models of object perception Daniel Kersten and Alan Yuilley The human visual system is the most complex pattern recognition device known. In ways that are yet to be fully understood, the visual cortex arrives at a simple and unambiguous i...
GeislerKerstennn0602-508.pdfPath: Minnesota >> GANDALF >> 0602 Fall, 2008
Description: news and views 2. Snyder, L. H., Batista, A. P. Goldberg, M. E. Annu. Rev. Neurosci. 22, 319349 (1999). 4. Culham, J. C. & Kanwisher, N. G. Curr. Opin. Neurobiol. 11, 157163 (2001)...
SchKerIJCV99.pdfPath: Minnesota >> GANDALF >> 99 Fall, 2008
Description: The Role of Task Specication in Optimal Cue Integration Paul R. Schrater and Daniel Kersten Department of Psychology, University of Minnesota, N218 Elliott Hall, 75 E. River Dr., Minneapolis, MN 55455, USA. Oct 28, 1999 Abstract. A full Bayesian...
KerSch99.pdfPath: Minnesota >> GANDALF >> 99 Fall, 2008
Description: Pattern inference theory: A probabilistic approach to vision Daniel Kersten and Paul Schrater August, 2001 To be published: Kersten, D., Heyer, D. (E...
KerSch99.psPath: Minnesota >> GANDALF >> 99 Fall, 2008
Description: Pattern inference theory:probabilistic h tovision A approac y Daniel ersten nd PaulSc K a hrater August, 001 2 To be published: Kersten, ., Heye...
SchraterKersten99.pdfPath: Minnesota >> GANDALF >> 99 Fall, 2008
Description: Statistical Structure and Task Dependence in Visual Cue Integration1 Paul R. Schrater and Daniel Kersten Department of Psychology, University of Minnesota, N218 Elliott Hall, 75 E. River Dr., Minneapolis, MN 55455, USA. February 28, 1999 Abstract A ...
SchraterKerstenCVPRWork99.pdfPath: Minnesota >> GANDALF >> 99 Fall, 2008
Description: Proceedings of the IEEE Workshop on Statistical and Computational Theories of Vision, Fort Collins, CO, June, 1999. (Published on Web). Statistical Structure and Task Dependence in Visual Cue Integration Paul R. Schrater1 and Daniel Kersten1 Abstra...
NIPS98.pdfPath: Minnesota >> GANDALF >> 98 Fall, 2008
Description: Computational Vision: Principles of Perceptual Inference Daniel Kersten Psychology, University of Minnesota NIPS*98 http:/vision.psych.umn.edu/www/kersten-lab/papers/NIPS98.pdf Announcements NIPS*98 Workshop on Statistical Theories of Cortical Func...
BibNIPS98.pdfPath: Minnesota >> GANDALF >> 98 Fall, 2008
Description: Bibliography Adelson, E. H. (1993). Perceptual organization and the judgment of brightness. Science, 262, 2042-2044. Adelson, E. H., & Bergen, J. R. (1991). The Plenoptic Function and the Elements of Early Vision. In M. M. Landy, A. (Ed.), Computatio...
yuicouker98.pdfPath: Minnesota >> GANDALF >> 98 Fall, 2008
Description: Computational Vision: Principles of Perceptual Inference , Alan L. Yuille James M. Coughlan, and Daniel Kersten November 25, 1998 This is the rst chapter from a book in preparation by the authors. Smith-Kettlewell Eye Research Institute, San Fra...
mamassianTICS1998.pdfPath: Minnesota >> GANDALF >> 1998 Fall, 2008
Description: Review Price Word comprehension sequence processing on phoneme monitoring Brain 117, 671682 48 Price, C.J. and Friston, K.J. (1997) Cognitive conjunctions: a new approach to brain activation experiments NeuroImage 5, 261270 49 De Renzi, E., Zambol...
CogNeuro98-final.pdfPath: Minnesota >> GANDALF >> 98 Fall, 2008
Description: 1 High-level Vision as Statistical Inference Daniel Kersten SHORT TITLE: Vision as Statistical Inference kersten@tc.umn.edu Department of Psychology, University of Minnesota, 75 East River Road,Minneapolis, MN, 55455. Kersten, D. (1999) The New C...
BrajeKerstenTarrTroje1999.pdfPath: Minnesota >> GANDALF >> 1999 Fall, 2008
Description: Braje, W.L., Kersten, D., Tarr, M.J. and Troje, N.F. Illumination effects in face recognition. (1998) Psychobiology. 26 (4), 371-380. Illumination Effects in Face Recognition Wendy L. Braje1 , Daniel Kersten2 , Michael J. Tarr3 , & Nikolaus F. Troje...
LiuKerstenKnillVR1999.pdfPath: Minnesota >> GANDALF >> 1999 Fall, 2008
Description: Vision Research 39 (1999) 603 612 Dissociating stimulus information from internal representation a case study in object recognition Zili Liu a,*, Daniel Kersten b, David C. Knill c a NEC Research Institute, 4 Independence Way, Princeton, NJ 08540...
LiuKerstenVR1998.pdfPath: Minnesota >> GANDALF >> 1998 Fall, 2008
Description: Vision Research 38 (1998) 2507 2519 2D observers for human 3D object recognition? Zili Liu a,*, Daniel Kersten b b a NEC Research Institute, 4 Independence Way, Princeton, NJ 08540, USA Department of Psychology, Uni6ersity of Minnesota, Minneapolis...
PhilTransRoy97Kersten-fin.pdfPath: Minnesota >> GANDALF >> 97 Fall, 2008
Description: Kersten, Daniel May 1998 Perceptual Categories for Spatial Layout Daniel Kersten Abstract The central problems of vision are often divided into object identication, and localization. Object identication, at least at ne levels of discrimination, m...
TarrKerstenBuelthoffVR1998.pdfPath: Minnesota >> GANDALF >> 1998 Fall, 2008
Description: Vision Research 38 (1998) 2259 2275 Why the visual recognition system might encode the effects of illumination Michael J. Tarr a,*, Daniel Kersten b, Heinrich H. Bulthoff c b a Department of Cogniti6e and Linguistic Sciences, Brown Uni6ersity, Box...
KerstenEtAlPerception1997.pdfPath: Minnesota >> GANDALF >> 1997 Fall, 2008
Description: Kersten, Mamassian David C. Knill Abstract We describe phenomenally strong visual illusions in which the motion of an object\'s cast shadow determines th...
LiuKnillKersten95.pdfPath: Minnesota >> GANDALF >> 95 Fall, 2008
Description: ...
KerstenJOSA87-600dpi.pdfPath: Minnesota >> GANDALF >> 87 Fall, 2008
Description: ...
KerstenThesisChap3.pdfPath: Minnesota >> GANDALF >> 3 Fall, 2008
Description: ...
KerstenThesisChap4.pdfPath: Minnesota >> GANDALF >> 4 Fall, 2008
Description: ...
sol_guide.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: How to write down a good solution? Before you read the proceeding you should know that writing down good solutions of math problems is not as hard as it might seem! There is just a couple of rules you have to follow, thats it! 1. A solution consists ...
1271sy.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: Math 1271 Lecturer: Professor Jiaping Wang Fall 2006 Office Hours: MWF 11:00am-12:00pm, Vincent Hall 230, 624-3829 E-mail: jiaping@math.umn.edu Web-page: www.math.umn.edu/~jiaping TAs: Li, Fang - (612) 625-0564, VinH 424, e-mail: lixx0539@umn.edu D...
1271hw.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: Assignment Schedule (2nd Edition) Math 1271 Fall 2006 - Calculus I: Lecture Section 050 Prof. Wang Vincent Hall 230 (612) 624-3829 Assigned Homework Problems Section 1.3 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.1 3.2 3.4 3.5 3.6 3.7 3.8 3.10 3.11 4.1 4....
1271_quiz_1_sol.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: 1271 Calculus I Quiz 1 September 12, 2006 Answer the questions in the space provided on the question sheets. On each question show all your work. Name and section: 1. (10 points) Explain how the following graphs are obtained from the graph y = f (...
1271_quiz_2_sol.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: 1271 Calculus I Quiz 2 September 19, 2006 Answer the questions in the space provided on the question sheets. On each question show all your work. Name and section: 1. (5 points) Determine the innite limit lim + x2 (x 2x =? + 2) x2 Solution: Sinc...
1271_quiz_3_sol.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: 1271 Calculus I Quiz 3 October 5, 2006 Answer the questions in the space provided on the question sheets. On each question show all your work. Name and section: 1. (a) (6 points) Find the derivative of the function f (x) = x + x using the denitio...
1271_quiz_4_sol.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: 1271 Calculus I Quiz 4 October 12, 2006 Answer the questions in the space provided on the question sheets. On each question show all your work. Name and section: 1. (10 points) Find the derivative of the function f (x) = 23 . x2 Solution: We use ...
1271_quiz_5_sol.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: 1271 Calculus I Quiz 5 November 2, 2006 Answer the questions in the space provided on the question sheets. On each question show all your work. Name and section: 1. (5 points) Show that the equation 2x 1 sin x = 0 has exactly one real root. (You...
1271_quiz_6_sol.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: 1271 Calculus I Quiz 6 November 9, 2006 Answer the questions in the space provided on the question sheets. On each question show all your work. Name and section: 1. (5 points) Find the asymptotes (vertical and horizontal) of y= x x1 Solution: Fir...
1271_quiz_7_sol.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: 1271 Calculus I Quiz 7 November 16, 2006 Answer the questions in the space provided on the question sheets. On each question show all your work. Name and section: 1. (10 points) A fence 8 ft tall runs parallel to a tall building at a distance of 4...
1271_midterm_1_sol_013_015.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: 1271 Calculus I Solutions - Midterm 1 September 26, 2006 1. Write the precise denition of xa lim f (x) = L. Solution: Denition: We say limxa = L if for any that if 0 < |x a| < then |f (x) L| < . 2. Evaluate > 0 there exists a > 0 such ex +...
1271_midterm_1_sol_053_055.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: 1271 Calculus I 1. Let Solutions - Midterm 1 3x2 + 7x 1 12x3 5x + 2 if x > 1 if x 1 September 26, 2006 f (x) = At what values of x is f (x) continuous? Discontinuous? Give reasons for your answer. Solution: Observe that except of the point x =...
1271_midterm_2_sol_013_015.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: 1271 Calculus I 1. Find f (x) if Solutions - Midterm 2 3ex . x+1 October 24, 2006 f (x) = Solution: We use the quotient rule and have f (x) = 3ex x+1 = (3ex ) (x + 1) 3ex (x + 1) (3ex )(x + 1) 3ex = = (x + 1)2 (x + 1)2 = 3xex . (x + 1)2 Gradin...
1271_midterm_2_sol_053_055.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: 1271 Calculus I Solutions - Midterm 2 October 24, 2006 1. In the implicit relationship 4x2 y 2 = 4 a) nd y as a function of x and y b) nd y as a function of y only. Solution: Dierentiate with respect to x. We get (4x2 y 2 ) = (4) , 8x 2yy = 0 W...
1271_midterm_3_sol_013_015.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: 1271 Calculus I 1. Find f (x) if Solutions - Midterm 3 x2 November 21, 2006 f (x) = x+1 t sin t dt Solution: Well use the fundamental theorem of calculus. We have x2 x2 0 x2 f (x) = x+1 t sin t dt = 0 t sin t dt + x+1 t sin t dt = 0 t ...
1271_midterm_3_sol_053_055.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: 1271 Calculus I Solutions - Midterm 3 November 21, 2006 1. Find the absolute maximum and minimum values of the function f (x) = 2x3 9x2 + 12x over the interval [0, 2]. Solution: The absolute extrema may occur either at the end-points of the inter...
1271_spr2003_final_sol.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: 1271 Calculus I Solutions - 2003 nal exam Multiple Choice Questions x2 +1 . x+7 1. Let f (x) = (A) (B) (C) (D) (E) 7 8 15 8 15 64 7 64 7 32 Then f (1) is equal to Solution: Compute f (x) = 2x(x + 7) (x2 + 1) x2 + 14x 1 = . (x + 7)2 (x + 7)2 Th...
review_sol_1_huiqiang.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: Solutions - Practice Midterm I 1. Start with the graph y = f (x) = 2 3 x. x, use transformations to sketch the graph of the function Solution: We take x and transform it to x. This ips the graph over the 3 x = x + 3 shifts now the graph 3...
review_sol_1_jiaping.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: Solutions - Practice Midterm I 1. Evaluate x1 lim 2 1 2 x1 x 1 Solution: We have x1 lim 1 2 x+1 2 2 = lim 2 = x1 (x 1)(x + 1) x1 x 1 x 1 x+12 x1 1 1 = lim = lim =. 21 x1 (x 1)(x + 1) x1 x + 1 x 2 = lim x1 2. Let f (x) = (x 1)3 (x + 1)3 if ...
review_sol_2_huiqiang.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: Solutions - Practice Midterm II 1. Let f (x) = x sin x 0 if x > 0, if x 0. Find f (0) if it exists or show why it doesnt exist. Solution: We use the denition of the derivative and get: f (0) = lim f (0 + h) f (0) =? h0 h Now, we look at one-sided...
review_sol_2_jiaping.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: Solutions - Practice Midterm II 1. For what values of x does the graph of f (x) = x3 + 3x2 + x + 3 have a horizontal tangent? Solution: In other words we look for points where f (x) = 0. Thus we compute f (x) = 3x2 + 6x + 1. Solve using the quadratic...
review_sol_3_huiqiang.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: Solutions - Practice Midterm III 1. Find the critical numbers of f (x) = x2 + 1 ; f (x) = x2 ex . x1 Solution: First, notice that for f (x) the domain is R \\ {1}. Let us nd f (x). Using the quotient rule we get f (x) = 2x(x 1) (x2 + 1) x2 2x 1 =...
review_sol_3_jiaping.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: Solutions - Practice Midterm III 1. Find 3 2 approximately by solving f (x) = 0 by Newtons method where f (x) = x3 2 and x1 = 1. Find x2 and x3 in the form of fractions. Solution: We build the sequence using the formula xn+1 = xn Compute f (x) = 3...
1051-syllabus.pdfPath: Minnesota >> MATH >> 018 Fall, 2008
Description: Fall 2008 MATH 1051 Precalculus I - Lec 010 Walter Rusin Syllabus This is the syllabus for the MATH 1051 Precalculus I lecture section 010 in Fall 2008. Time: MWF 10:10AM-11:00AM Place: Rapson Hall 100 Contact Information: Instructor: Walter Ru...