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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
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Last Name:
First Name:
Your OSU ID Number:
Your Recitation time starts at circle one: 12 PM (noon) 2 PM 4 PM
Instructions:
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.
Rn (x) = f (n+1)^ (c) (x − a)n+ (n + 1)!
for some c between a and x.
n=1 an^ converges by the integral test and^ an^ =^ f^ (n), then Z (^) ∞
N +
f (x) dx ≤ S − SN ≤ aN +1 +
N+
f (x) dx
and 0 ≤ S − UN ≤ aN + where UN = SN +
N+
f (x) dx.