MTH 306 Final Exam Fall 2008: Mathematics Exam with Error Estimates, Exams of Mathematics

A final exam for a university-level mathematics course, mth 306, held in fall 2008. The exam consists of 12 problems worth 5 points each. Six problems are multiple choice, three problems involve identifying true or false statements, and three problems are long-answer problems. Students are not allowed to use books or notes during the exam, but they may use a calculator for standard numerical calculations. The exam covers error estimates, including the taylor polynomial error estimate, integral test error estimate, and the alternating series error estimate.

Typology: Exams

Pre 2010

Uploaded on 08/30/2009

koofers-user-hwm-1
koofers-user-hwm-1 🇺🇸

9 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
MTH 306 FINAL EXAM FALL 2008
Last Name:
First Name:
Your OSU ID Number:
Your Recitation time starts at circle one: 12 PM (noon) 2 PM 4 PM
Instructions:
There are 12 problems worth 5 points each. Some problems have parts.
Six problems are multiple choice. This means there is one correct answer and you must circle the
correct answer to receive any credit.
Three problems list five statements. You must mark the letter T next to each true statement and the
letter F next to each false statement in the space provided next to each statement. You will
earn 1point for each correctly marked response.
Three problems are long-answer problems where you may earn partial credit depending on your work.
Each problem has a space in which to write your answer. Expect to lose credit if you do not put
your answer in the space provided. Space also is provided for you to show your supporting work.
Expect to receive no credit for a correct answer that your work does not support. This
means that you must present the mathematical reasoning needed to justify your answers.
You may use any correct method to solve a particular problem, unless that problem directs otherwise.
You may use a calculator for standard numerical calculations but not for symbolic dierentiation,
integration, or other calculus operations. You may use the calculator to check your work, but on the
long-answer questions you must include the mathematical reasoning needed to obtain any
answer you give just as if you didn’t have a calculator available during the exam. Iwant
to know what you know, not what your calculator knows.
Give exact answers whenever possible. Decimal approximations to answers that can be given exactly
will not receive full credit.
Solve the problems in the order that is easiest for you. Skip problems that you find harder and come
back to them later.
The exam is closed book and no notes are allowed.
GOOD LUCK!
Problem 12345678910 11 12 Tota l
Score
Hint. The space provided for your required work or scratch work should be adequate for solving each
problem. If you find the space provided inadequate you can be reasonably sure there is another way to solve
the problem.
1
pf2

Partial preview of the text

Download MTH 306 Final Exam Fall 2008: Mathematics Exam with Error Estimates and more Exams Mathematics in PDF only on Docsity!

MTH 306 FINAL EXAM FALL 2008

Last Name:

First Name:

Your OSU ID Number:

Your Recitation time starts at circle one: 12 PM (noon) 2 PM 4 PM

Instructions:

  • There are 12 problems worth 5 points each. Some problems have parts.
  • Six problems are multiple choice. This means there is one correct answer and you must circle the correct answer to receive any credit.
  • Three problems list five statements. You must mark the letter T next to each true statement and the letter F next to each false statement in the space provided next to each statement. You will earn 1 point for each correctly marked response.
  • Three problems are long-answer problems where you may earn partial credit depending on your work. Each problem has a space in which to write your answer. Expect to lose credit if you do not put your answer in the space provided. Space also is provided for you to show your supporting work. Expect to receive no credit for a correct answer that your work does not support. This means that you must present the mathematical reasoning needed to justify your answers.
  • You may use any correct method to solve a particular problem, unless that problem directs otherwise.
  • You may use a calculator for standard numerical calculations but not for symbolic differentiation, integration, or other calculus operations. You may use the calculator to check your work, but on the long-answer questions you must include the mathematical reasoning needed to obtain any answer you give just as if you didn’t have a calculator available during the exam. I want to know what you know, not what your calculator knows.
  • Give exact answers whenever possible. Decimal approximations to answers that can be given exactly will not receive full credit.
  • Solve the problems in the order that is easiest for you. Skip problems that you find harder and come back to them later.
  • The exam is closed book and no notes are allowed.
  • GOOD LUCK!

Problem 1 2 3 4 5 6 7 8 9 10 11 12 Total

Score

Hint. The space provided for your required work or scratch work should be adequate for solving each problem. If you find the space provided inadequate you can be reasonably sure there is another way to solve the problem.

You may use the following reminders related to error estimates. However, for each error estimate you need to know the circumstances under which it can be applied.

  • (Taylor Polynomial Error Estimate) For Taylor polynomials with base point a

Rn (x) = f (n+1)^ (c) (x − a)n+ (n + 1)!

for some c between a and x.

  • (Integral Test Error Estimate) If a series

P∞

n=1 an^ converges by the integral test and^ an^ =^ f^ (n), then Z (^) ∞

N +

f (x) dx ≤ S − SN ≤ aN +1 +

Z ∞

N+

f (x) dx

and 0 ≤ S − UN ≤ aN + where UN = SN +

Z ∞

N+

f (x) dx.

  • (Alternating Series Error Estimate) You should be able to remember the error estimate associated with the alternating series test. It will not be provided on the exam.