# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

8 Pages

### fa07hw7

Course: MATH 1120, Fall 2008
School: Cornell
Rating:

Word Count: 262

#### Document Preview

If 5. x = 3 sin 2t, y = 3 cos 2t, (0 t /3), then x 2 + y 2 = 9. This is part of a circle. y t=0 x 2 +y 2 =9 x t= 3 Fig. 2-5 7. If x = 3 sin t, y = 4 cos t, (-1 t 1), then y2 x2 + = 1. This is an ellipse. 9 16 y t=0 x 2 y2 9 + 16 =1 x t=-1 t=1 Fig. 2-7 9. If x = cos3 t, y = sin3 t, (0 t 2 ), then x 2/3 + y 2/3 = 1. This is an astroid. y t=/2 x 2/3 +y 2/3 =1 t= t=0 t=2 t=3/2 Fig. 2-9 21. y = x 3...

Register Now

#### Unformatted Document Excerpt

Coursehero >> New York >> Cornell >> MATH 1120

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
If 5. x = 3 sin 2t, y = 3 cos 2t, (0 t /3), then x 2 + y 2 = 9. This is part of a circle. y t=0 x 2 +y 2 =9 x t= 3 Fig. 2-5 7. If x = 3 sin t, y = 4 cos t, (-1 t 1), then y2 x2 + = 1. This is an ellipse. 9 16 y t=0 x 2 y2 9 + 16 =1 x t=-1 t=1 Fig. 2-7 9. If x = cos3 t, y = sin3 t, (0 t 2 ), then x 2/3 + y 2/3 = 1. This is an astroid. y t=/2 x 2/3 +y 2/3 =1 t= t=0 t=2 t=3/2 Fig. 2-9 21. y = x 3 , 0 x 1. ds = 1 + 9x 4 d x. The area of the surface of rotation about the x-axis is 1 S = 2 0 x 3 1 + 9x 4 d x u du = Let u = 1 + 9x 4 du = 36x 3 d x = 18 10 1 (103/2 - 1) sq. units. 27 23. If y = x 3/2 , 0 x 1, is rotated about the y-axis, the surface area generated is 1 S = 2 0 x 1+ 9x dx 4 Let u = 1 + du = 9 dx 4 9x 4 32 81 32 = 81 = = 81 13/4 64 1 (u - 1) u du 13/4 1 2 5/2 2 3/2 u - u 5 3 (13/4)5/2 5 -1 - (13/4)3/2 - 1 3 sq. units. 25. If y = sin x, 0 x , is rotated about the x-axis, the surface area generated is S = 2 0 1 sin x 1 + cos2 d x 1 + u 2 du -1 /4 Let u = cos x du = - sin x d x = 2 = 2 -/4 Let u = tan du = sec2 d /4 0 /4 0 sec3 d = 4 sec3 d = 2 sec tan + ln | sec + tan | = 2 2 + ln(1 + 2) sq. units. 27. For y = x3 1 + , 1 x 4, we have 12 x 1 x2 + 2 d x. ds = 4 x The surface generated by rotating the curve about the y-axis has area 4 S = 2 1 x 1 x2 + 2 4 x dx = 2 = 2 4 x4 + ln |x| 16 1 255 + ln 4 sq. units. 16 3. If x = 1/t, y = t - 1, (0 < t < 4), then y = y 1 4 ,3 t=4 1 - 1. This is part of a hyperbola. x 1 y= x - 1 t=1 x y=-1 Fig. 2-3
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Cornell - MATH - 1120
15. The volume remaining isbV = 2axh 1 - x2 x3 - 2 3bx bb adx= 2 ha3 2 = h(b2 - a 2 ) - h b2 - 3 b 3 1 2a = h b2 - 3a 2 + cu. units. 3 by hx y b + h =1x=a xdx b xFig. 1-156. Rotate about a) the x-axis1V =0(x 2 - x 4
Cornell - MATH - 1120
12. The exact value of I is I =01x3 x dx = 321=01 . 3The approximation is T1 = (1) 1 2 1 2 1 (0) + (1) = . 2 2 2The actual error is I - T1 = - 1 . However, since 6 f (x) = x 2 , then f (x) = 2 on [0,1], so the error estimate here giv
Cornell - MATH - 1120
9.x -2 dx +x -2 x -2 =x- d x. x2 + x - 2 A B Ax - A + B x + 2B x -2 = + = , then A+B = 1 and - A+2B = -2, If 2 x +x -2 x +2 x -1 x2 + x - 2 so that A = 4/3 and B = -1/3. Thus 1- x2 x2 dx 4 1 dx dx =x- + x2 + x - 2 3 x +2 3 x -1 1 4 = x - ln |x + 2|
Cornell - MATH - 1120
6. sin x dx x Let u = x dx du = 2 x=2sin u du = -2 cos u + C = -2 cos x + C.5. =x dx (4x 2 + 1)5 1 8Let u = 4x 2 + 1 du = 8x d x -1 1 + C. u -5 du = - u -4 + C = 32 32(4x 2 + 1)42. =cos(ax + b) d x1 a 1 = sin(ax + b) + C. aLe
Wisconsin Milwaukee - MATENG - MAT201
CHAPTER 21OPTICAL PROPERTIESPROBLEM SOLUTIONS21.1 Similarities between photons and phonons are: 1) Both may be described as being wave-like in nature. 2) The energy for both is quantized. Differences between photons and phonons are: 1) Phonons
Wisconsin Milwaukee - MATENG - MAT201
CHAPTER 19THERMAL PROPERTIESPROBLEM SOLUTIONS19.1 The energy, E, required to raise the temperature of a given mass of material, m, is the product of the specific heat, the mass of material, and the temperature change, T, asE = cpm(T)The T is
Wisconsin Milwaukee - MATENG - MAT201
CHAPTER 17CORROSION AND DEGRADATION OF MATERIALSPROBLEM SOLUTIONS17.1 (a) Oxidation is the process by which an atom gives up an electron (or electrons) to become a cation. Reduction is the process by which an atom acquires an extra electron (or
Wisconsin Milwaukee - MATENG - MAT201
CHAPTER 14POLYMER STRUCTURESPROBLEM SOLUTIONS14.1Polymorphism is when two or more crystal structures are possible for a material of given composition. Isomerism is when two or more polymer molecules or mer units have the same composition, but
Wisconsin Milwaukee - MATENG - MAT201
CHAPTER 12STRUCTURES AND PROPERTIES OF CERAMICSPROBLEM SOLUTIONS12.1The two characteristics of component ions that determine the crystal structure are:1) themagnitude of the electrical charge on each ion; and 2) the relative sizes of the
Wisconsin Milwaukee - MATENG - MAT201
CHAPTER 10PHASE TRANSFORMATIONS IN METALSPROBLEM SOLUTIONS10.1 The two stages involved in the formation of particles of a new phase are nucleation and growth. The nucleation process involves the formation of normally very small particles of the
Wisconsin Milwaukee - MATENG - MAT201
CHAPTER 7DISLOCATIONS AND STRENGTHENING MECHANISMSPROBLEM SOLUTIONS7.1 The dislocation density is just the total dislocation length per unit volume of material (in this case per 3 5 -2 cubic millimeters). Thus, the total length in 1000 mm of ma
Wisconsin Milwaukee - MATENG - MAT201
CHAPTER 5DIFFUSIONPROBLEM SOLUTIONS5.1 Self-diffusion is atomic migration in pure metals-i.e., when all atoms exchanging positions are of the same type. Interdiffusion is diffusion of atoms of one metal into another metal.5.2 Self-diffusion m
Wisconsin Milwaukee - MATENG - MAT201
CHAPTER 3THE STRUCTURE OF CRYSTALLINE SOLIDS PROBLEM SOLUTIONS 3.1 Atomic structure relates to the number of protons and neutrons in the nucleus of an atom, as well as the number and probability distributions of the constituent electrons. On the ot
Wisconsin Milwaukee - CIVENG - CE202
Cornell - MATH - 2940
Cornell - MATH - 2940
Math 294 Homework 4Section 3.3 28. Form a 4 X 4 matrix A with the given vectors as its columns. The matrix A reduces to 1 0 0 2 0 1 0 3 . 0 0 1 4 0 0 0 k - 29 This matrix can be reduced further to I4 if and only if k = 29. By Summary 3.3.9, t
Cornell - MATH - 2940
Math 294 - HW9 Solutions 7.1 Discrete Dynamical Systems5. Assume Av = v and Bv = v for some eigenvalues , . The (A + B)v = Av + Bv = v + v = ( + )v so v is an eigenvector of A + B with eigenvalue + .6. Yes. If Av = v and Bv = v, then ABv = A(v)
Cornell - MATH - 2940
Math 294 - HW5 Solutions 4.1 Introduction to Linear Spaces 4. The subset V is a subspace of P2 : The neutral element f (t) = 0 (for all t) is in V since1 1 00dt = 0.1 Let f and g be in V . By the definition of V , 0 f dt = 0 and 0 gdt = 0. We
Cornell - HD - 1150
Andrew Bernstein HD 116 Section October 18, 2007 Qingfang Song Understanding and Critiquing a Journal Article I Wish I Were a Warrior: The Role of Wishful Identification in the Effects of Violent Video Games on Aggression in Adolescent BoysElly Kon
Cornell - COMM - 101.2
Andrew Bernstein September 27, 2007 COM L 108.01 Essay 3 FinalAlea: Memories of Underdevelopment FinalAleas film, Memories of Underdevelopment, is a social commentary on the effects of the Socialist Revolution on one man. It illustrates how Sergi
Michigan State University - CE - 337
CHARACTERISTICS OF SOILSPhysical characteristics Engineering characteristicsPHYSICAL CHARACTERISTICS OF SOILS Grain size distribution Atterberg limits CompactionATTERBERG LIMITS &amp; THE UNIFIED SOIL CLASSIFICATION SYSTEM (USCS)ATTERBERG LIMIT
USC - PHIL - 140g
PHIL 140 Professor Gideon Yaffe TA: Eduardo Villanueva Thomson's Claims on Abortion and Self-Defense There is much to discuss pertaining to the topic that we as a society have coined &quot;philosophy.&quot; Anything that stands up to logic can be viewed in phi
Wisconsin Milwaukee - CIVENG - CE250
Wisconsin Milwaukee - CIVENG - CE490
Wisconsin Milwaukee - CIVENG - CE335
Wisconsin Milwaukee - CIVENG - CE372
Wisconsin Milwaukee - MECHENG - MECH301
Wisconsin Milwaukee - MECHENG - MECH301
Wisconsin Milwaukee - MECHENG - MECH301
Wisconsin Milwaukee - MECHENG - MECH301
Wisconsin Milwaukee - MECHENG - MECH301
Wisconsin Milwaukee - MECHENG - MECH301
Wisconsin Milwaukee - MATENG - MAT201
CHAPTER 22ECONOMIC, ENVIRONMENTAL, AND SOCIETAL ISSUES IN MATERIALS SCIENCE AND ENGINEERINGPROBLEM SOLUTION22.D1W The three materials that are used for beverage containers are glass, aluminum, and the polymer polyethylene terephthalate (designa
Wisconsin Milwaukee - MATENG - MAT201
CHAPTER 15 CHARACTERISTICS, APPLICATIONS, AND PROCESSING OF POLYMERSPROBLEM SOLUTIONS15.1 From Figure 15.3, the elastic modulus is the slope in the elastic linear region of the 20C curve, which is(stress) 30 MPa - 0 MPa = = 3.3 GPa (strain) 9 x
Wisconsin Milwaukee - MATENG - MAT201
CHAPTER 8FAILUREPROBLEM SOLUTIONS8.1 Several situations in which the possibility of failure is part of the design of a component or product are as follows: (1) the pull tab on the top of aluminum beverage cans; (2) aluminum utility/light poles
Wisconsin Milwaukee - CIVENG - CE202
Cornell - MATH - 2940
Michigan State University - CE - 337
Weight-Volume Phase DiagramModule-ILearning Objectives Be able to convert volume to mass and vice-versa. Be familiar with the FPS and SI units for mass and volume computations. Be familiar with the different phases in a soil mass and their sign
Michigan State University - CE - 337
FLOW OF WATER THROUGH POROUS MEDIAFLOW CHARACTERISTICSFlow Classification Steady flow the flow conditions are constant over time Unsteady flow the flow conditions change over time Flow Types One dimensional flow, the flow parameters (pressure
Michigan State University - CE - 337
WATER IN SOILS Effect of water on soils can be dramatic. Numerous soil failures are caused by water actions Examples of water-related soil failures Static soil-water interaction Dynamic flow of water through soils; seepage forcesSOIL FAILURE CA
Michigan State University - CE - 337
CHARACTERISTICS OF SOILSPhysical characteristics Engineering characteristicsPHYSICAL CHARACTERISTICS OF SOILS Grain size distribution Atterberg limits CompactionCOMPACTIONSOIL COMPACTIONIn the field In the labCOMPACTION Compaction is so
Cornell - MATH - 1120
19. Apply the ratio test to(-1)n(x - 1)n : 2n + 3 (x - 1)n+1 2n + 3 = |x - 1|. 2n + 5 (x - 1)n = limThe series converges absolutely if |x - 1| &lt; 1, that is, if 0 &lt; x &lt; 2, and converges conditionally if x = 2. It diverges for all other values
Cornell - MATH - 1120
3. y = 2 x 3/2 , y = x, ds = 1 + x d x 3 8 8 2 52 1 + x d x = (1 + x)3/2 = L= units. 3 3 0 05.2 -1/3 x , 3 4 9x 2/3 + 4 dx ds = 1 + x -2/3 d x = 9 3|x|1/3 1 9x 2/3 + 4 d x Let u = 9x 2/3 + 4 L=2 3x 1/3 0 du = 6x -1/3 d x 1 13 2(133/2 ) - 16
Cornell - MATH - 1120
9.x sin-1 x d x U = sin-1 x dx dU = 1 - x2 1 1 = x 2 sin-1 x - 2 2 = dV = x dx x2 V = 2 2 dx x Let x = sin 1 - x2 d x = cos d1 1 2 -1 x sin x - sin2 d 2 2 1 2 -1 1 = x sin x - ( - sin cos ) + C 2 4 1 2 1 1 = x - sin-1 x + x 1 - x 2 + C. 2
Wisconsin Milwaukee - MATENG - MAT201
CHAPTER 20MAGNETIC PROPERTIESPROBLEM SOLUTIONS20.1 (a) We may calculate the magnetic field strength generated by this coil using Equation (20.1) asNI lH ==(200 turns)(10 A) = 10,000 A - turns/m 0.2 m(b) In a vacuum, the flux density is
Wisconsin Milwaukee - MATENG - MAT201
CHAPTER 13APPLICATIONS AND PROCESSING OF CERAMICSPROBLEM SOLUTIONS13.1 The two desirable characteristics of glasses are optical transparency and ease of fabrication.13.2 (a) Devitrification is the process whereby a glass material is caused to
Wisconsin Milwaukee - MATENG - MAT201
CHAPTER 6 MECHANICAL PROPERTIES OF METALSPROBLEM SOLUTIONS6.1This problem asks that we derive Equations (6.4a) and (6.4b), using mechanics of materials principles. In Figure (a) below is shown a block element of material of cross-sectional area
Cornell - MATH - 2940
Cornell - HD - 1150
Andrew Bernstein Cornell UniversityAugust 19, 2007 Summer ReadingThe Pickup by Nadine GordimerEven in post-apartheid South Africa, de facto racial segregation and discrimination were rampant. It was far easier for rich white people from favorabl
Cornell - COMM - 101.2
Andrew Bernstein COM L 108.01 Subdesarrollo: Chronic Underdevelopment in CubaSeptember 6, 2007 Sarah PickleThroughout Memories of Underdevelopment, by Edmundo Desnos, the narrator (Sergio in the film-the names will be used interchangeably to illu
Cornell - NS - 1150
Does creatine increase athletic performance? The effectiveness of creatine as an athletic training supplement is widely debated in the scientific community today. One side firmly believes that its use will increase performance in high intensity aerob
Cornell - ENGL - 185.9
Schlegel's Influence on the Validity of Kafka's WritingsAlthough writing and living more than a century apart, Franz Kafka and Friedrich Schlegel developed the same central theme of failure of communication into all of their writings. Although many
Cornell - FREN - 2090
mon avis et l'avis de notre invite francophone, la vie d'un immigre n'est pas facile. Il est ncessaire d'ajouter beaucoup de choses comme la nourriture, la culture, et la langue. Les immigres font un grande effort d'assimiler a la culture de leur p
Cornell - FREN - 2090
Que pensez-vous des mdias amricains? Donner deux exemples pris dans l'actualit. 250 mots. A mon avis, les mdias amricains placent trop d'importance sur les personnes clbre. Les clbrits gardaient plus d'importance que les chefs internationaux. La majo
Cornell - ENGL - 185.9
&quot;The Great Wall of China&quot;In Franz Kafka's short story The Great Wall of China, the reader is presented with an allegorical account of a man leaving his home and loved ones in the south of China to partake in the building of the Great Wall in the nor
Wisconsin Milwaukee - CIVENG - CE202
Wisconsin Milwaukee - CIVENG - CE202
Wisconsin Milwaukee - CIVENG - CE202
Wisconsin Milwaukee - CIVENG - CE202
Cornell - MATH - 2940
Math 294 - HW1 Solutions 1.1 Introduction to Linear Systems 26. The system reduces to x - 3z y + 2z (k 2 - 4)z = = = 1 1 . k-2This system has a unique solution if k 2 - 4 = 0, that is, if k = 2. If k = 2, then the last equation is 0 = 0, and there
Cornell - MATH - 2940