{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MATH118FS05N - Name(Print UW Student Id Number University...

Info icon This preview shows pages 1–14. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
Image of page 11

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 12
Image of page 13

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 14
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Name (Print): UW Student Id. Number: University of Waterloo Final Examination ' Math 118 Calculus 2 for Engineering Instructor: See table below Date: Wednesday, August 3, 2005 Term: 1055 Number of exam pages: 14 (including cover page) Section: See table below Time: 12:30 — 3:00 p.m. Duration of exam: 2.5 hours Exam type: Closed book Additional material allowed: No calculators or additional material allowed Circle your instructor’s name and section number Instructor R. André R. André J. West B. Richmond Instructions . Write your name and ID number on this page. . Questions are to be answered in the space provided. Give REASONS for your answers and show all your work required to obtain your answers. If the space is insufficient, use the back and indicate where your work continues. ' . There are 14 pages in this examination. Check that you have all the pages. Write your name at the top of each page. . No calculators or additional aids allowed. Section 001 002 003 004 Question Mark 1 /10 Math 118 Final Exam, Spring 2005 Page 2 of 14 Name: [7] 1. General short answer questions. (a) What technique would you use to evaluate f xexdm? (b) In the my—plane, the curve of the parametric equations x(t) = 400st y(t) = 2 sint can be described by which of the following: (Circle the correct answer) (i) a circle (ii) an ellipse (iii) a spiral (iv) a parabola. (c) Consider the recursive sequence defined by cn+1 = V1 + c" with cl = 1. If the sequence is and monotone, then it converges. (d) Assuming the sequence in(c) converges, find its limit. (e) For what values of 19 does 22:1 nip converge? (f) Is f3" sin mdw = 0 true or false? (g) Is the following true or false? 5 1 d 2— —1—15=—4-3l 1: /0(.’E—1)2m (27 ) '0 + Math 118 Final Exam, Spring 2005 Page 3 of 14 Name: [10] 2. Evaluate the following integrals. (a) :1: 1v+1‘ /$2_4da: Math 118 Final Exam, Spring 2005 Page 4 of 14 Name: [4] 3. Sketch the cardioid 7" = 1 + cos 0, and write down the formula for its area specifying the limits of integration. his not neccessary for you to simplify or evaluate the integral. [10] 4. Convergence of series. Determine if the given series converges: (a) °° 1 Z n(ln n)2 n=2 Math 118 Final Exam, Spring 2005 Page 5 of 14 Name: (b) Math 118 Final Exam, Spring 2005 Page 6 of 14 Name: [5] 5. Convergence of power series. Determine the radius of convergence and interval of convergence of .. 00 n ——2 1 E (—3 ) —:c". n=l Tl, (Be sure to test the endpoints of the interval.) Math 118 Final Exam, Spring 2005 Page 7 of 14 Name: [12] 6. Taylor and Maclaurin series applications. (a) Give the Maclaurin series for the functions 1 1 and " 1+t \/1+t3' Math 118 Final Exam, Spring 2005 Page 8 of 14 Name: (b) Find the Maclaurin series for (0) Assuming that we have determined the radius of convergence of the Maclaurin series in b) to be equal to 1 write an infinite series which can be used to approximate the value of 1/2 1 / dt. 0 V 1 + t3 Math 118 Final Exam, Spring 2005‘ Page 9 of 14 Name: [12] 7. Taylor series and Taylor polynomial approximations. (a) Give the Binomial series formula including the interval of convergence. (b) Find the first 5th order Taylor polynomial of the Maclaurin series generated by the function f(a:) 2 V1 +23. Math 118 Final Exam, Spring 2005 Page 10 of 14 Name: (c) Write out an expression for the 5th order Taylor polynomial evaluated at 0.01 for the Maclau— rin series in part b). Do not compute its value. (d) If you use the 5th order Taylor polynomial evaluated at 0.01 to approximate the value of \/ 1.01 give an upper bound for the error. Do not simplify your upper bound expression. (e) Given the function f (11:) = sina: use the Taylor Remainder Formula to compute an upper bound for the error if we use the 5th order Taylor polynomial of the Maclaurin series generated by sinx to approximate the value of sin 0.1. Do not simplify your upper bound expression. Math 118 Final Exam, Spring 2005 Page 11 of 14 Name: [8] 8. Differential equations. Solve the following differential equations for y in terms of 3:: (a) dy ___= 2 2 ydx (11 +1) Math 118 Final Exam, Spring 2005 l Page 12 of 14 Name: [12] 9. Newtonian mechanics. A rock whose mass is 75 kg is dropped from a helicopter hovering 2000 m above the ground and falls toward the ground under the influence of gravity. Assume that the force due to air resistance is proportional to the velocity of the rock, with the proportionality constant 191 = 30 kg/sec. You may approximate the gravitational acceleration to be 10m/52. (a) Set up a differential equation which, when solved, will give us the velocity v(t) of the rock at time t. Do not solve this differential equation. (b) Suppose the general solution to the differential equation in part a) is v(t) = 25 — %e(”2/5)‘ Where M is any nonzero number. Find the velocity at 1 second after the rock is dropped. Do not simplify your answer. Math 118 Final Exam, Spring 2005 Page 13 of 14 Name: (c) Find an expression for the distance $(t) between the rock and the helicopter at time t. Your expression for a;(t) should not contain any parameters. ' Math 118 Final Exam, Spring 2005 Page 14 of 14 Name: [Blank page] ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern