Mathematics & Statistics Texas Tech University Kent Pearce Department of Mathematics and Statistics Texas Tech University Lubbock, Texas 79409-1042 Voice: (806)742-2566 x 226 FAX: (806)742-1112 Email: kent.pearce@ttu.edu

 Math 1352 Calculus II Spring 2008 Strauss, Bradley, Smith Calculus 5th Prentice Hall

Review Exam III
 Section Content Suggested Problems Section 8.1 sequences limits of sequences limit theorems for sequences monotone sequences, bounded sequences, BMCT limits of special sequences 12, 16, 19, 20, 23, 24, 26 Section 8.2 infinite series definition of convergence linearity geometric series 6, 8, 13, 20, 24, 28, 31, 48 Section 8.3 divergence test series with non-negative terms integral test p-series 13, 15, 21, 23, 24, 28, 32, 33, 45 Section 8.4 direct comparison test limiit comparison test 13, 16, 19, 22, 24, 27, 31, 37, 45, 48 Section 8.5 ratio test root test 5, 8, 11, 14, 17, 20, 24, 29, 31, 36, 39, 43 Section 8.6 alternating series test error estimates via alternating series test definition of absolute convergence absolute convergence implies convergence generalized ratio and root test table 8.1: summary of convergence tests 6, 9, 10, 16, 19, 23, 33, 35, 38, 40, 41 Section 8.7 definition of power series (centered at x=c) convergence of power series (on intevals) radius of convergence of a power series interval of convergence term-by-term differentiation of power series term-by-term integration of power series 3, 6, 11, 19, 25, 27, 29, 37, 42 Section 8.8 nth-degree approximating Taylor's polynomial at x=c Taylor's series at x=c MacLaurin series remainder function at x=c Taylor's theorem representation and uniqueness of representation Taylor's series for standard functions (table 8.2) approximation and error estimates manipulation of Taylor's series 4, 7, 11, 20, 21, 25, 32, 34, 38, 52, Chapter Review: Supplementary Problems 2, 5, 9, 14, 19, 26, 28, 31, 32, 33, 36, 41, 45, 52, 55, 56, 58, 61, 63, 68, 75

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