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Calc1Test3

Course: MATH 1431, Spring 2010
School: U. Houston
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Test 5/10/10 Print 4:48 PM PRINTABLE VERSION Test 3 You scored 40 out of 40 Question 1 Your 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 between the graph of f and the x -axis on [0, 1] is 1, and the area bounded between the graph of f and the x -axis on [1, 2] is 1. Determine a)...

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Test 5/10/10 Print 4:48 PM PRINTABLE VERSION Test 3 You scored 40 out of 40 Question 1 Your 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 between the graph of f and the x -axis on [0, 1] is 1, and the area bounded between the graph of f and the x -axis on [1, 2] is 1. Determine a) https://www.casa.uh.edu/CourseWare/Root/UsersStudents/PrintTest.htm Page 1 of 7 Print Test 5/10/10 4:48 PM b) c) d) e) Question 2 Your answer is CORRECT. The function k is an antiderivative of the continuous function g, and the function f is an antiderivative of the continuous function h. Also, Compute a) b) c) d) e) Question 3 Your answer is CORRECT. Find the average value of the function on the interval [-1, 3]. https://www.casa.uh.edu/CourseWare/Root/UsersStudents/PrintTest.htm Page 2 of 7 Print Test 5/10/10 4:48 PM a) b) c) d) e) Question 4 Your answer is CORRECT. Compute a) b) c) d) e) Question 5 Your answer is CORRECT. This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. https://www.casa.uh.edu/CourseWare/Root/UsersStudents/PrintTest.htm Page 3 of 7 Print Test 5/10/10 4:48 PM Problem Code: 521 Compute a) b) I have placed my work and my answer on my answer sheet. I want to have points deducted from my test for not working this problem. Question 6 Your answer is CORRECT. This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 613 Given Part a: Sketch the graph of the function with rectangles drawn to represent the lower sum of f over the interval [-2, 2] with respect to the partition P = {-2,0, 1, 2} then compute the lower sum, Lf(P). Part b: Sketch the graph of the function with rectangles drawn to represent the upper sum of f over the interval [-2, 2] with respect to the partition P = {-2,0, 1, 2} then compute the upper sum, Uf(P). a) b) I have placed my work and my answer on my answer sheet. I want to have points deducted from my test for not working this problem. Question 7 Your answer is CORRECT. This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) your on answer sheet for full credit. Problem Code: 712 Let https://www.casa.uh.edu/CourseWare/Root/UsersStudents/PrintTest.htm Page 4 of 7 Print Test 5/10/10 4:48 PM Give the derivative of F at x = 8 a) b) I have placed my work and my answer on my answer sheet. I want to have points deducted from my test for not working this problem. Question 8 Your answer is CORRECT. This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 815 Find the function f that satisfies these conditions: a) b) I have placed my work and my answer on my answer sheet. I want to have points deducted from my test for not working this problem. Question 9 Your answer is CORRECT. This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 939 The graph of the region bounded by f ( x ) = 2 - x 2 and g( x ) = - x is shown below: https://www.casa.uh.edu/CourseWare/Root/UsersStudents/PrintTest.htm Page 5 of 7 Print Test 5/10/10 4:48 PM Part a: Give a formula in terms of x -integral(s) for the area of this region. Do not compute the area. Part b: Give a formula in terms of y -integral(s) for the area of this region. Do not compute the area. a) b) I have placed my work and my answer on my answer sheet. I want to have points deducted from my test for not working this problem. Question 10 Your answer is CORRECT. This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1042 The region bounded by f ( x ) = x 2 and g( x ) = 3x is rotated around the x-axis. The graph of the region is shown below https://www.casa.uh.edu/CourseWare/Root/UsersStudents/PrintTest.htm Page 6 of 7 Print Test 5/10/10 4:48 PM Part a: Give a formula involving integral(s) with respect to x for the volume generated. Do not compute the volume. Part b: Give a formula involving integral(s) with respect to y for the volume generated. Do not compute the volume. a) b) I have placed my work and my answer on my answer sheet. I want to have points deducted from my test for not working this problem. https://www.casa.uh.edu/CourseWare/Root/UsersStudents/PrintTest.htm Page 7 of 7
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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U. Houston - MATH - 3321
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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 :
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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
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