finalreview - MAT 132 Calculus II Final Exam Topics This is...

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Unformatted text preview: MAT 132 Calculus II Final Exam Topics This is the description of problems that may appear on the final exam. (The actual practice questions can be found in the textbook or past homework or exams.) The goal of this list is to help you to focus on essential skills and to streamline your exam preparation. The list below is quite large; not all questions below will be included, those that will be included may contain fewer parts, and the questions and their parts might be arranged differently; for example, there may be a true-false question based on these topics. Topics not listed below will not be included in the test. 1. Determine whether a given sequence • is increasing, decreasing, or neither (for simple sequences only; you must under- stand the concept, but calculations will not be required) • converges or diverges • if converges, find limit 2. Determine whether a given series ∑ a n is convergent or divergent. Use one of the following convergence tests (listed here for your reviewing convenience, won’t be listed on exam). • divergence test • alternating series test • ratio test • comparison/limit comparison • integral test • is it one of the standard series: geometric, p-series? 3. For a given power series • find the radius of convergence • indicate on the x-axis where the series converges, and where it diverges • indicate points that require further testing • check whether the series converges at those points (or at some other points) 4. For a given function, find the Taylor series centered at a given point (say at x = 0 or x = 3). You may be asked to use any method, or specifically one of the following. • use the Taylor series formula • use algebraic manipulations with geometric series 5. Use series to • compute limits • express an integral as series 6. Compute given integrals (definite or indefinite). Use the following methods (listed for your reviewing convenience; no hints will be given on the test, except perhaps for trigonometry)....
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This note was uploaded on 11/30/2011 for the course MAT 203 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.

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finalreview - MAT 132 Calculus II Final Exam Topics This is...

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