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141 MATH EXAMINATION 2 March 28, 2002 NAME STUDENT NUMBER INSTRUCTOR SECTION NUMBER There are 7 multiple choice questions. For each problem five possible answers are given, only one of which is correct. You should solve the problem and circle the letter of the answer that you wish to give. Circle only one choice. There is 1 set of determine the convergence questions. You should circle the correct choice. Circle...
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141 MATH EXAMINATION 2 March 28, 2002
NAME STUDENT NUMBER INSTRUCTOR SECTION NUMBER
There are 7 multiple choice questions. For each problem five possible answers are given, only one of which is correct. You should solve the problem and circle the letter of the answer that you wish to give. Circle only one choice. There is 1 set of determine the convergence questions. You should circle the correct choice. Circle only one choice. There is 1 one choice. se...
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Penn State - MATH - 141
Math 141 Exam 2 Spring 2002 Answers1.b, 2.e, 3.d, 4.b, 5.a, 6.d, 7.a 8.(a) CC, (b) AC, (c) D, (d) AC 9.(a) F, (b) T, (c) F, (d) F 10.(a) converges to 1, (b) diverges, (c) diverges 11. The series diverges by the limit comparison test (and the p-serie
Penn State - MATH - 141
MATH 141 EXAMINATION II NOVEMBER 7, 2001NAME STUDENT NUMBER INSTRUCTOR SECTION NUMBERThere are eight multiple-choice problems worth 5 points each, 2 problems consisting of several short-answer questions, and 4 partial credit problems where you sh
Penn State - MATH - 141
Math 141 Exam 2 Fall 2001 Answers(from the 2002-2003 supplement)1.b, 2.c, 3.d, 4.c, 5.b, 6.a, 7.e, 8.b 9. T, F, T, F 10. converges absolutely, converges conditionally, diverges 11. e2 12. - 1 2
Penn State - MATH - 141
MATH 141 SECOND MIDTERM PENN STATE UNIVERSITY MARCH 28, 2001Name: . ID Number:. Instructor:. Class Section:..5 pts1. Evaluate 5x2 . x0 1 - cos x lim a) -10 b) 0 c) 1 d) 10 e) PAGE 2 5 pts2. Order the functions 3x , x3 , log3 x from slowest
Penn State - MATH - 141
Math 141 Exam 2 Spring 2001 Answers(from the Nittany Lion version of the old text)1.a, 2.d, 3.b, 4.c, 5.b, 6.e, 7.d, 8.e 9. T, F, T, F 10. diverges, converges absolutely, converges conditionally 11. converges (integral test) 12. converges to -2 (t
Penn State - MATH - 141
CHAPTER 77.1 Inverse Functions One-to-one functions, inverse functions and the formula (f -1 ) (a) = 1 . f (f -1 (a)7.2 Exponential Functions Properties of exponentials and the derivative formulas d x e = ex dx together with the corresponding inte
Penn State - MATH - 141
MATH 141 FINAL EXAMINATION MAY 4, 2004 TEST FORM DNAME STUDENT NUMBER INSTRUCTOR SECTION NUMBERThis examination consists of 20 problems. The first 14 are multiple choice questions, the next two are short answer questions and the remaining 4 are p
Penn State - MATH - 141
Math 141 Final Exam Spring 2004 Answers (Form D)1.c, 2.a, 3.b, 4.e, 5.c, 6.a, 7.d, 8.d, 9.b, 10.d, 11.b, 12.e, 13.c, 14.a 15.(a) AC, (b) AC, (c) D, (d) CC 16.(a) diverges, (b) converges to 2, (c) converges to 1 17. x - 2 x + C 18. R= 9 , I: -6 < x
Penn State - MATH - 141
Math 141 Final Exam Fall 2003 Answers1.a, 2.e, 3.d, 4.a, 5.a, 6.b, 7.b, 8.d, 9.c, 10.b, 11.a, 12.b, 13.c, 14.b 15. -2 16. 4 -4 e417.(a) CC, (b) AC, (c) AC 18. Be sure you've used two integrals and limits. 2n-119.(a) sin(2x) = (-1)n 22n-1 x-
Penn State - MATH - 141
MATH 141FINAL EXAMINATIONDecember 18, 2002NameID #Section #There are 12 multiple choice questions (1 through 12). For each of them five possible answers are given, only one of which is correct. You are to circle the letter corresponding t
Penn State - MATH - 141
Math 141 Final Exam Fall 2002 Answers1.b, 2.d, 3.a, 4.b, 5.c, 6.b, 7.c, 8.c, 9.c, 10.b, 11.c, 12.e 13.(a) CC (b) D (c) AC 14.(a) must diverge (b) must converge (c) must converge 15. x tan-1 x - 1 ln(1 + x2 ) + C 2 16. 1 (1 - x2 )3/2 - 1 - x2 + C 3 1
Penn State - MATH - 141
MATH 141 FINAL EXAMINATION SPRING 2000NAME STUDENT NUMBER INSTRUCTOR SECTION NUMBERBe sure to code accurately your student I.D. number on the answer sheet. Blacken the corresponding circles completely. Code your section number on the scantron usi
Penn State - MATH - 141
Math 141 Final Exam Spring 2000 Answers1.d, 2.d, 3.b, 4.a, 5.e, 6.b, 7.e, 8.b, 9.c, 10.e, 11.a, 12.e, 13.b, 14.d 15. AC, D, D, CC 16. T3 (x) = 1 - (x - 1) + (x - 1)2 - (x - 1)3 17.1 x tan-1 x + +C 2 + 1) 2 2(x18.(a) converges by the (direct) comp
Penn State - MATH - 141
Algebra Practice with Logarithms1) Change each exponential equation into an equivalent equation involving a logarithm, and vice-versa. a) 9 = 32b) x2=c) log2 = xd) ln x = e2) Find the exact value of each logarithm. (No calculators!) a
Penn State - MATH - 141
Math 141 Power Series Review1) Find the radius and interval of convergence of each power series. (-1)n xn n2 +3 3n xn n! nn (x-3)n (n-1)2n (3x-2)n n3/2 4n+1a)n=0b)n=0 c)n=1 n=0d)n=22) Suppose thatn=0 cn 3n converges andcn 5
Penn State - MATH - 141
Math 141 Final Exam Spring 2002 Answers1.d, 2.d, 3.a, 4.e, 5.a, 6.b, 7.b, 8.c, 9.b, 10.a, 11.d, 12.b, 13.b, 14.a, 15.a, 16.a, 17.c, 18.b 19.1 2 sin-1 x - 1 x 1 - x2 + C 220. x tan x + ln | cos x| + C 21. radius of convergence: 1 , interval of c
Carnegie Mellon - BIO - 03510
Computational Biology, Part 11 GenefindingRobert F. Murphy Copyright 1997, 2001, 2003-2007. All rights reserved.Clues to locations of genes (Prokaryotic Signals)sfor Transcriptionx Promoters x Transcription factor binding sitessfor Transl
Carnegie Mellon - BIO - 03510
Computational Biology, Part 12 Predicting from Protein SequenceRobert F. Murphy Copyright 1996, 1999-2007 All rights reserved.1Starting PointsBroad Goal: To determine or predict as much as we can from a "new" protein sequence s Have covered h
Carnegie Mellon - BIO - 03510
Computational Biology, Part 13 Retrieving and Displaying Macromolecular StructuresRobert F. Murphy Copyright 1996, 1999, 2001-2007. All rights reserved.1Retrieving 3D structuressProtein Data Bank (PDB)x home page = http:/www.rcsb.org/pdb/s
Carnegie Mellon - BIO - 03510
Computational Biology Part 22 Biological Imaging IE. Glory, G. Steven Vanni Meel Velliste, Robert F. Murphy Copyright 1998, 2000-2007. All rights reserved.Biological imagingsSignificant advances in the fields of optics and electronics in the p
ASU - ECN - 470
TOPIC I INTRODUCTION AND SET THEORY[1] Introduction Economics Vs. Mathematical Economics. "Income positively affects consumption. Consumption level can never be negative. The marginal propensity consume is less than one." C = a + bY, where a >
ASU - ECN - 470
TOPIC II EQUILIBRIUM MODELS[1] Concept of Equilibrium Equilibrium: A state without tendency to change.EX 1:EX 2:II-1 Types of Equilibrium Stable Equilibrium: Once out of equilibrium, there is a tendency to go back. Unstable Equilibrium:
ASU - ECN - 470
TOPIC III LINEAR ALGEBRA[1] (1) 1) Linear Equations Case of Two Endogenous Variables Linear vs. Nonlinear Equations Linear equation: Nonlinear equation: ax + by = c, where a, b and c are constants. ax2 + by = c. Can express a linear equation by
ASU - ECN - 470
[6]VectorDefinition: Vector is a n1 or 1n matrix.Note: Vector is usually expressed by the form of (1,1) or (1,1) row vector;1 . 11 column vector. 1 When people talk about vectors, they are usually column vectors. Vector arithmetics f
ASU - ECN - 470
TOPIC IV CALCULUS[1] Limit Suppose that we have a function y = f(x). What would happen to y as x xo?Definition: Let y = f(x). Then, the limit value of y as x a is denoted by limxaf(x). EX 1: y = 1 + 2x. y = 1/x, x 0.As x 0, y 1. limx0y =
ASU - ECN - 470
TOPIC V COMPARATIVE STATICS[1] MotivationP SD(Y1) D(Yo) Q Here, D(Yo) denotes the demand curve when Y = Y o. Similarly, D(Y1) denotes the demand curve when Y = Y1. Observe that as Y changes, P and Q change. In economic models, equilibrium
ASU - ECN - 470
TOPIC VII UNCONSTRAINED OPTIMIZATION II[1] Relative Maximum and Minimum(1)Review for y = f(x): f(x) = 0 get x*. f(x*) > 0 x* is relative min. point. f(x*) < 0 x* is relative max. point. FOC: SOC:(2)For y = f(x1,x2,.,xn): FOC:f f f
ASU - ECN - 470
1. Matrix Algebra and Linear Economic ModelsReferences Ch. 1 3 (Turkington); Ch. 4 5.2 (Klein). [1] Motivation One market equilibrium Model Assume perfectly competitive market: Both buyers and sellers are price-takers. Demand: Qd = a + bP , a >
Texas A&M - GEOL - 648
Stable Isotope Geology GEOL 648Fall, 2007 E. GrossmanANALYSIS OF CARBONATES ON DELTAPLUSXP AND GAS BENCH II LAB 2The purpose of this lab is to perform carbon and oxygen isotopic analyses of carbonate minerals using the Gas Bench II system and D
ASU - ECN - 470
2. Further Topics in Matrix Algebra(1) Quadratic Form Consider: a11 a12 . a1n x1 a x a22 . a2 n 21 ; xn1 = 2 , = [aij ] = : : : : an1 an 2 . ann xn Annwhere A is symmetric ( aij = a ji ). The following form is called a qua
ASU - ECN - 470
S. C. AHNASSIGNMENT 1 Due February 16 (Monday)1998, SPRING1. (10 pts.) Let S1 = {3,6,9} and S2 = {a,b}. Is {(3,a),(6a),(9,a)} a function from S1 to S2. Why or why not? Explain. 2. (10 pts.) Suppose that the domain of the function y = x 2 - x +