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### Quiz 3

Course: MATH 1431, Spring 2010
School: U. Houston
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Test 3/6/10 Print 1:57 PM PRINTABLE VERSION Quiz 3 You scored 100 out of 100 Question 1 Your answer is CORRECT. The graph of the function f is given below, On which of the following intervals is f continuous? a) b) c) d) e) ( -1, 3] [5, 8) ( -4, -1] [ -1, 3) [3, 5) https://www.casa.uh.edu/CourseWare/Root/UsersStudents/PrintTest.htm Page 1 of 11 Print Test 3/6/10 1:57 PM Question 2 Your answer is...

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U. Houston - MATH - 1431
Print Test3/6/10 1:58 PMPRINTABLE VERSIONQuiz 4You scored 100 out of 100Question 1Your answer is CORRECT.Given thatand c = 5, find f ' ( c ) by forming the difference quotientand taking the limit as h0.a)b)c)d) e) Question 2Your answer is C
U. Houston - MATH - 1431
Print Test3/6/10 1:59 PMPRINTABLE VERSIONQuiz 5You scored 100 out of 100Question 1Your answer is CORRECT.Find .a) b) c) d) e) Question 2Your answer is CORRECT.Find .a)https:/www.casa.uh.edu/CourseWare/Root/UsersStudents/PrintTest.htm Page 1 of
U. Houston - MATH - 1431
Print Test4/4/10 1:21 AMPRINTABLE VERSIONQuiz 6You scored 100 out of 100Question 1Your answer is CORRECT.Calculate the derivative of the given function:a) b) c) d) e) Question 2Your answer is CORRECT.Calculate the derivative of the given functio
U. Houston - MATH - 1431
Print Test4/4/10 1:22 AMPRINTABLE VERSIONQuiz 7You scored 100 out of 100Question 1Your answer is CORRECT.Use differentials to estimate the value indicated.a)b)c) d)e) Question 2Your answer is CORRECT.Use differentials to estimate the value in
U. Houston - MATH - 1431
Print Test4/4/10 1:23 AMPRINTABLE VERSIONQuiz 8You scored 100 out of 100Question 1Your answer is CORRECT.Find the critical numbers of f and classify all local extreme values.a) b) c) d) e)Critical nos. Critical nos.1; local max f (-1) = -19; loc
U. Houston - MATH - 1431
Print Test4/26/10 10:20 PMPRINTABLE VERSIONQuiz 9You scored 100 out of 100Question 1Your answer is CORRECT.Describe the concavity of the graph of f and find the points of inflection (if any).a) b) c) d) e)concave down on (concave up on (concave u
U. Houston - MATH - 1431
Print Test4/26/10 10:20 PMPRINTABLE VERSIONQuiz 11You scored 100 out of 100Question 1Your answer is CORRECT.Evaluate the definite integral:a)b)c)d) e) Question 2Your answer is CORRECT.Evaluate the definite integral:a)https:/www.casa.uh.edu/
U. Houston - MATH - 1431
Print Test3/6/10 1:54 PMPRINTABLE VERSIONTest 1You scored 60 out of 60Question 1Your answer is CORRECT.Evaluate the following limit:a) b) c) d)e) Question 2Your answer is CORRECT.Evaluate the following limit:a)b) c)https:/www.casa.uh.edu/Cou
U. Houston - MATH - 1431
PRINTABLE VERSIONTest 1You scored 54 out of 72Question 1Your answer is INCORRECT.Computea) b) c) d) e) f ) None of the above. Question 2Your answer is CORRECT.Computea) b) c) d) e) f ) None of the above. Question 3Your answer is CORRECT.Compute
U. Houston - MATH - 1431
U. Houston - MATH - 1431
Print Test4/11/10 9:02 PMPRINTABLE VERSIONTest 2You scored 30 out of 30Question 1Your answer is CORRECT.Determine the interval(s) at which f ( x ) is concave up.a) b) c) d) e)( -5, (-, -5), (3, ) , -3), (5,))( -5, 3) (, 3)Question 2Your ans
U. Houston - MATH - 1431
PRINTABLE VERSIONTest 2You scored 50 out of 70Question 1Your answer is CORRECT.Use differentials to estimate the square root of 37. Hint: Do you know the square root of a number close to 37?a)b)c)d)e) f ) None of the above. Question 2Your answe
U. Houston - MATH - 1431
Print Test5/10/10 4:48 PMPRINTABLE VERSIONTest 3You scored 40 out of 40Question 1Your answer is CORRECT.The graph of f is shown below on the interval [-1, 2].The area bounded between the graph of f and the x -axis on [-1, 0] is 9, the area bounded
U. Houston - MATH - 1431
PRINTABLE VERSIONTest 3You scored 50 out of 50Question 1Your answer is CORRECT.Find the average value of the function on the interval [-2,1]. a) b) c) d) e) f ) None of the above. Question 2Your answer is CORRECT.LetGive the derivative of F at x =
U. Houston - MATH - 1431
PRINTABLE VERSIONFinalYou scored 80 out of 110Question 1Your answer is INCORRECT.Determine whether it is possible to find a value B so that the functionis continuous. a) b) c) d) e) f ) None of the above. Question 2Your answer is CORRECT.Computea
U. Houston - MATH - 1431
Print Test5/14/10 1:36 PMPRINTABLE VERSIONFinalYou scored 90 out of 90Question 1Your answer is CORRECT.Compute the limit:a)b) c) d)e) Question 2Your answer is CORRECT.Suppose that for a function f , f (3) is not defined. Also suppose that and
U. Houston - MATH - 3321
Answers to Odd-Numbered ProblemsCHAPTER 1 Exercises 1.1 1. (a) ordinary, rst order (c) partial, second order (e) ordinary, third order (g) ordinary, second order 3. Both y and z are solutions. 5. Both y and z are solutions. 7. Both u1 and u2 are solution
U. Houston - MATH - 3321
CHAPTER 4The Laplace Transform4.1 IntroductionThe Laplace transform provides an eective method of solving initial-value problems for linear dierential equations with constant coecients. However, the usefulness of Laplace transforms is by no means restr
U. Houston - MATH - 3321
DIFFERENTIAL EQUATIONSBasic TerminologyA dierential equation is an equation that contains an unknown function together with one or more of its derivatives.1Examples1.y = 2x + cos x2.dy = ky dt3.x2y 2xy + 2y = 4x34. 2u 2u + =0 2 2 x y5.d2y dy
U. Houston - MATH - 3321
CHAPTER 1Introduction to Dierential Equations1.1 Basic TerminologyMost of the phenomena studied in the sciences and engineering involve processes that change with time. For example, it is well known that the rate of decay of a radioactive material at t
U. Houston - MATH - 3321
FIRST ORDER EQUATIONSF (x, y, y ) = 0Basic assumption: This equation can be solved for y ; that is, the equation can be written in the form y = f (x, y ) (1)1I. First Order Linear EquationsEquation (1) is a linear equation if f has the form f (x, y )
U. Houston - MATH - 3321
Second Order Linear Dierential EquationsA second order linear dierential equation is an equation which can be written in the form y + p(x)y + q (x)y = f (x) where p, q , and f (1)are continuousfunctions on some interval I .The functions p and q are ca
U. Houston - MATH - 3321
CHAPTER 3Second Order Linear Dierential Equations3.1 Introduction; Basic Terminology and ResultsAny second order dierential equation can be written as F (x, y, y , y ) = 0 This chapter is concerned with special yet very important second order equations
U. Houston - MATH - 3321
The Laplace TransformLetfbe continuous function on The Laplace transform of[0, ).f , denoted by L[f (x)], or by F (s), is given byL[f (x)] = F (s) = sx e f (x) dx. 0The domain of F is the set of real numbers s for which the improper integral conve
U. Houston - MATH - 3321
Systems of Linear Algebraic EquationsExample Solve the system x + 2y 5z = 1 3x 9y + 21z = 0 x + 6y 11z = 1 x + 2y 5z = 1 y 2z = 1 z = 1 Solution set: x = 4, y = 1, z = 11The Elementary OperationsThe operations that produce equivalent systems are calle
U. Houston - MATH - 3321
CHAPTER 5Linear Algebra5.1 IntroductionLinear algebra is an important mathematical subject independent of its connection to dierential equations. However, it is the relation between dierential equations and linear algebra that is important to us and so
U. Houston - MATH - 3321
Systems of Linear Dierential EquationsI. Converting a linear equation to a linear systemConsider the third-order equation y or y = r (t)y q (t)y p(t)y + f (t). + p (t )y + q (t )y + r (t )y = f (t )1Introduce new dependent variables x1, x2, x3, as fol
U. Houston - MATH - 3321
CHAPTER 6Linear Dierential Systems6.1 Higher-Order Linear Dierential EquationsThis section is a continuation of Chapter 3. As you will see, all of the theory that we developed for second-order linear dierential equations carries over, essentially verba
U. Houston - MATH - 3321
The Complex Number System The need for extending the real number system is evident when considering solutions of simple equations. For example, the equation x2 + 1 = 0 has no real number solutions, for if x is any real number, then x2 0 and so x2 + 1 1. W
U. Houston - MATH - 3321
MATH 3321 1. ln x dx = x (a) ln(ln x) + C (b) (d)1 2EMCF Quiz 11/20/10(ln x)2 (ln x)2 + C(c) (ln x) + C1 2(e) None of the above.2.dx = 4 + x2 (a) (b) (d)1 2 1 2ln(4 + x2) + C tan1 x + C tan1 (x/2) + C(c) tan1 (x/2) + C1 2(e) None of the abov
U. Houston - MATH - 3321
MATH 3321Quiz 21/26/101. If 2 + 3 = 10, 6 + 5 = 66, 8 + 4 = 96, and 3 + 6 = 27, then 9 + 6 =? (a) 122 (b) 108 (c) 135 (d) 152 (e) None of the above. 2. x dx = 9 x2 x +C 3 (b) (9 x2 )1/2 + C x (c) x sin1 +C 3 (d) 9 x2 + C (a) sin1 (e) None of the above.
U. Houston - MATH - 3321
MATH 3321 1. xy = x2y + 2x3y 2 is (a) a linear equation. (b) a separable equation. (c) a Bernoulli equation. (d) a homogeneous equation. (e) none of the above.Quiz 32/1/102. xy = x3 2x2y is (a) a linear equation. (b) a separable equation. (c) a Bernoul
U. Houston - MATH - 3321
MATH 3321Quiz 42/3/10 1 1 y = 2 + 2, x x y (1) = 0,1. If y = y (x) is the solution of the initial-value problem y + then y (e) =: (a) (b) (c) (d) (e) 1 +e e e 1 e2 1 e e None of the above. dy 3y = x3y 1/3 is: dx2. The general solution of x (a) y 1/3 =
U. Houston - MATH - 3321
MATH 3321Quiz 52/14/101. The general solution of y 2y 15y = 0 is: (a) y = C1 e5x + C2e3x (b) y = C1 e5x + C2 e3x (c) y = C1 e5x + C2e3x (d) y = C1 e5x + C2e3x (e) None of the above.2. The solution of the initial-value problem y + 8y + 16y = 0, y (0) =
U. Houston - MATH - 3321
MATH 3321Quiz 62/22/101. If y = y (x) is a solution of x2y + 6xy + 6y = 0, then lim y (x) = (Hint: the equation x has solutions of the form y = xr .) (a) (b) 1 (c) 0 (d) Does not exist. (e) None of the above. 2. If y = y (x) is the solution of the init
U. Houston - MATH - 3321
MATH 3321Quiz 73/4/101. If f (x) = 2e3x + cos 2x + 3x, then L[f (x)] = (a) (b) (c) (d) (e) 2 3 2 +2 +2 s3 s +4 s s 3 2 +2 +2 s+3 s +4 s s 3 2 +2 +3 s3 s +4 s 2 3 2 +2 + s+3 s +4 s None of the above.2. If f (x) = 2e2x sin 3x 2xe3x + 4, then L[f (x)] =
U. Houston - MATH - 3321
MATH 3321Quiz 810/15/091. Set f (x) = 2xex + 4 cos 2x + 2x. L[f (x)] = 2s 2 2 +2 +3 (s + 1) s + 4 s 4 2 2 +2 (b) +2 2 (s 1) s +4 s 2 2 4s +2 (c) +2 2 (s + 1) s +4 s 4 2 2s +2 (d) +2 (s + 1)3 s + 4 s (a) (e) None of the above.2. Set f (x) = 4 cosh x 3x
U. Houston - MATH - 3321
MATH 3321 1. Set f (x) = x2 + 2, x,Quiz 9 0x&lt;1 x1 1 s2 1 s2 1 s2 1 s2 1 s 2 + s 3 s 2 s + . L[f (x)] =3/22/10(a) (b) (c) (d) (e)3 2 2 + es 3 3 s s s 2 2 2 + es 3 + 3 s s s 2 2 1 + es 3 + 3 s s s 2 2 2 + es 3 3 s s s None of the above.2. Set f (x) =
U. Houston - MATH - 3321
MATH 3321 1 3 1. If A = 2 2 , B = 4 0 then d23 = (a) 1 (b) 17 (c) 9 (d) 17 (e) None of the above. Quiz 10 3 2 2 0 4 24/7/10 2 3 0 , C = 4 2 3 , and D = AB 3C , 0 1 32. If A is 2 3, B is 3 4, C is 4 2, and D is 3 2, then ABC + 2D is: (a) 2 2 (b) 3 2 (c
U. Houston - MATH - 3321
MATH 3321Quiz 114/12/091. If a system of n linear equations in n unknowns is consistent, then the rank of the matrix of coecients is n. (a) Always true (b) Sometimes true (c) False (d) None of the above2. If the determinant of the matrix of coecients
U. Houston - MATH - 3321
MATH 3321Quiz 124/19/101. If a system of n linear equations in n unknowns has innitely many solutions, then the rank of the matrix of coecients is n 1. (a) Always true. (b) Sometimes true. (c) Never true. (d) None of the above.2. If 0 is an eigenvalue
U. Houston - MATH - 3321
MATH 3321Quiz 134/22/101. If 0 is not an eigenvalue of the matrix of coecients of a homogeneous system of n linear equations in n unknowns, then the system has innitely many solutions. (a) Always true. (b) Sometimes true. (c) Never true. (d) None of th
U. Houston - MATH - 3321
Exam 1 Review Show that y = y(x) is/is not a solution of the differential equation F (x, y, y , . . . y (n) = 0. Examples: 1. x2 y - 3x y + 4y = 0; 2. d3y dy + = ex ; 3 dx dx y1 (x) = x2 , y2 (x) = x2 ln xy(x) = 1 + sin x + 1 ex , z(x) = 2 cos x + 1 ex .
U. Houston - MATH - 3321
ANSWERS Exam 1 ReviewPart I. y is/is not a solution. 1. Both are solutions. 2. Both are solutions. 3. y1 is a solution, y2 is not. 4. Both are solutions. 5. y is a solution. Part II. Find the dierential equation. 1. 2xyy = 3y 2 + 6. 2. x2y xy 3y = 0. 3.
U. Houston - MATH - 3321
MATH 3321 Sample Questions for Exam 2 Linear Nonhomogeneous Dierential Equations 1. Find the general solution of y 4 6 4 y + 2 y = 2. x x x2. Find the general solution of y + 4 y = 2 tan 2x. 3. Find the general solution of y 6 y + 9 y = 4 e3x + 4. Find t
U. Houston - MATH - 3321
MATH 3321 Sample Questions for Exam 2Linear Nonhomogeneous Dierential Equations 1. Find the general solution of y Answer y = C1 x2 + C2 x3 + 2 . 3 2. Find the general solution of y + 4 y = 2 tan 2x. Answer y = C1 cos 2x + C2 sin 2x 1 24 6 4 y + 2 y = 2
U. Houston - MATH - 3321
MATH 3321 Sample Questions for Exam 3 2x 4 3 5x 3y 2 2 y 5 2 5 121. Find x and y so that+=.2. Let A =2 1 3 0 4 2,B=3 1 25,3 2 C = 0 1 . 1 2 (b) AB (c) B + AC (d) CBAPerform the indicated operations, if possible: (a) AC3. Show that the matrix
U. Houston - MATH - 3321
MATH 3321 Sample Questions for Exam 31. Find x and y so that2x 4 3 5x+3y 2 2 y=5 2 5 12.Answer: x = 31/17, y = 49/17 2 1 3 0 4 2 3 1 25 3 2 C = 0 1 . 1 2 (b) AB (c) B + AC (d) CBA 2. Let A =,B=,Perform the indicated operations, if possible:
U. Houston - MATH - 3321
MATH 3321 Final Exam Sample Questions 1. y 2 = Cx3 3 is the general solution of a dierential equation. Find the equation. Answer y = 3y 2 + 9 2xy cos 2x . x22. Find the general solution of x y + 3 y = Answer y = sin 2x C + 3. 2x3 x3. Find the general so
U. Houston - MATH - 3321
MATH 3321 ENGINEERING MATHEMATICS Homework Problems Chapter 1 Exercises 1.1: 1, 2, 3, 4, 7, 9, 10, 12, 13, 14, 16, 17, 18, 21, 22 Exercises 1.3: 2, 3, 6, 7, 8, 9, 11, 14, 15, 16, 17, 18, 20, 21, 24 Chapter 2 Exercises 2.1: 2, 3, 4, 7, 9, 11, 14, 17, 18, 2
U. Houston - MATH - 3321
POLYNOMIALSDenition 1: A real polynomial is an expression of the form P (x) = an xn + an1 xn1 + + a1 x + a0 where n is a nonnegative integer and a0 , a1, . . . , an1, an are real numbers with an = 0. The nonnegative integer n is called the degree of P .
U. Houston - MATH - 3321
Higher-Order Linear Differential Equationsnth order linear differential equation: (1) y(n) + pn1( x) y(n1) +L+ p1( x) y '+ p0 ( x) y = f ( x) where p0 , p1, K, pn1, and f are continuous functions on some interval I .(1) is homogeneous if f ( x) 0 on I :
U. Houston - MATH - 3321
Table of Integrals 1. 3. 5. 7. 9. 11. 13. 15. 17. 19. 21. ur du = ur+1 + C, r+1 r = 1 2. 4. 6. 8. 10. 12. 14. 16. 18. 1 u2 + C u2 1| + C 20. 1 du = ln |u| + C u sin u du = cos u + C tan u du = ln | sec u| + C sec u du = ln | sec u + tan u| + C sec u tan u
U. Houston - MATH - 3321
1.If a system of n linear equa-tions in n unknowns is consistent, then the rank of the matrix of coefcients is n.1. Always true2. Sometimes true3. False12.If the determinant of thematrix of coecients of a system of n linear equations in n unknown
U. Houston - POLS - 1336
1 .The US Constitution is the oldest and shortest constitution still in effect today.Student Response Value True 100%Score: 1.5/1.52 .Early Supreme Court decisions (to 1835) expanded the power of the national government at the expense of state govern
U. Houston - POLS - 1336
1 .Match 8th and 9th amendment cases with their proper descriptionStatement Response Value Griswold v. Connecticut 1963 Established Right to Privacy 11.11% Roe v. Wade 1973 Legalized 1st trimester abortions 11.11% Webster 1989 outlawed 1 abortion method
U. Houston - POLS - 1336
1 .While politically significant, talk show format is one of the least popular on radio.Student Response Value False 100%Score: 2/22 .Until the 1980s, there were federal laws whichStud ent Resp onse Valu e A. limit ed how many medi a outlet s one co
U. Houston - POLS - 1336
1 .In Texas, any party which receives at least 20% of the vote for governor must use primary elections to nominate their candidates for public (elected) office.Student Response Value True 100%Score: 1/12 .The Republican front-runner for the 1968 pres
U. Houston - CHEM - 1331
Blackboard Learning System5/9/10 3:39 PMYour location: Home Page Exams Final_Exam Assessments View All Submissions View AttemptView Attempt 1 of 1Title: Started: Submitted: Time spent: Final_Exam May 7, 2010 11:01 AM May 7, 2010 12:55 PM 01:54:11 Tota
U. Houston - CHEM - 1331
Blackboard Learning System3/6/10 2:03 PMYour location: Home Page Exams Midterm_Exam_1 Assessments View All Submissions View AttemptView Attempt 1 of 1Title: Started: Submitted: Time spent: Midterm_Exam_1 February 23, 2010 1:05 PM February 23, 2010 2:1
U. Houston - CHEM - 1331
JumptoNavigationFrameViewAttempt1of1Title: Started: Submitted: Timespent: Totalscore: 1.Yourlocation:AssessmentsViewAllSubmissionsViewAttemptMidterm_Exam_1 September28,200911:27AM September28,200912:26PM 00:58:23 18/20=90% Totalscoreadjustedby0.0 Ma