General Information
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The exam will be held on Thursday, April 25, from 5:30pm to 7:00pm, in Swords 328.
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Plan to arrive a few minutes early to allow time to distribute the exams.
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The exam will cover material from sections 7.7, 7.8, 7.9, 10.1, 10.2, 10.3, 10.4, and 10.5 in the text.
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Cell-phones should be turned OFF for the duration of the exam.
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You may use a non-graphing, scientific calculator during the exam. No other calculator or electronic device may be used during the exam.
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This is a closed-book exam. No books or notes may be used during the exam.
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You will be expected to show all of your work. A correct answer with insufficient justification
may not receive full credit.
Topics
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Improper Integrals. (7.7) Know how to express an improper integral as a limit, and compute the resulting expression.
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Probability. (7.8) Know how to use a probability density function for a random variable to calculate the probabilities, mean and median. Be familiar with and know how to use the formulas for the exponential probability densitiy. You will be provided with a table of values of probabilities associated with the standard normal density function. You should know how to use these values to calculate probabilities associated with an arbitrary normal density.
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Numerical Integration. (7.9) Know how to calculate the Trapezoid Rule and Simpson's Rule approximations of a definite integral. Know and be able to use the error bounds for these approximations. (Theorems 1 and 2)
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Sequences. (10.1) Know how to calculate limits of sequences. Also know and be able to use the basic properties of limits. (Recursively defined sequences will not be covered on this exam.)
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Summing Infinite Series (10.2) Know the definition of convergence of an infinite series (on p. 524) in terms of its partial sums. Be able to simplify the partial sums of a telescoping series. Know when a geometric series converges and when it diverges, and what its sum is if it converges. Know what the nth term test says (and also what is doesn't say!).
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Convergence Tests (10.3, 10.4, 10.5) Know how to use the integral test to determine if a series converges or diverges. Know when a p-series converges. Know how to use the direct comparison and limit comparison tests to determine if a series converges or diverges. (I'll expect you to state briefly why the series you are comparing with converges or diverges (p-series or geometric), and verify that the hypotheses of the test are satisfied.) Know how to use the Absolute Convergence Test (Theorem 1 in 10.4), and the Alternating Series Test to determine if a series converges (note that neither of these can be used to conclude a series diverges). Know how to use the Alternating Series Error Bound (Theorem 3 in 10.4). Finally, know how to use the Ratio Test to determine if a series converges or diverges.
Preparing for the Exam
Here are a some problems to use for practice. Solutions to the odd-numbered exercises are in the back of the text.
Section 7.7, p. 422
Exercises 5, 7, 13, 15, 19, 21, 25, 27, 29, 79, 81
Section 7.8, p. 429
Exercises 1, 3, 5, 7, 11, 17, 21
Section 7.9, p. 438
Exercises 5, 7, 9, 11, 13, 15, 17, 19, 37, 39, 43, 53
Section 10.1, p. 521
Exercises 1, 3, 5, 17, 21, 23, 25, 27, 29, 35, 37, 43, 45, 65
Section 10.2, p. 530
Exercises 3, 11, 13, 17, 23, 25, 27, 29, 31, 33, 43, 47, 57
Section 10.3, p. 539
Exercises 1, 3, 5, 7, 9, 11, 15, 17, 21, 39, 41, 49, 51, 53, 55, 59, 61, 77
Section 10.4, p. 546
Exercises 3, 5, 7, 13, 17, 21, 23, 25
Section 10.5, p. 546
Exercises 1, 7, 9, 13, 15, 17, 23, 25, 51
Here is an exam given in a previous year: Practice Exam
