General Information
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The exam will be held on Thursday, April 27, from 5:30pm to 7:00pm, in Smith Labs 155 (note the change in location - this is the room next door to from where the first two exams were held).
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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, 8.1, 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 exponential and normal probability densities. 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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Arc Length and Surface Area (8.1) Know the formulas for arc length of a graph (Theorem 1) and the area of a surface of revolution (Equation 3), and be able to set up and compute the resulting integrals for a given function.
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Sequences. (10.1) Know how to calculate limits of sequences given by a formula. 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 (as in Example 1, and Homework 8, 3(e)). 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 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 thr 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 from the Chapter Review sections to use for practice. Solutions to the odd-numbered exercises are in the back of the text.
Chapter 7 Review, p. 440
Exercises 69-73, 75-84, 99-104, 106-107, 109
Chapter 8 Review, p. 476
Exercises 1-5, 7-10
Chapter 10 Review, p. 476
Exercises 3-11, 13-15, 17-18, 27-33, 36-48, 51, 61a, 65-72
