Geometric Series – Far Out An instructive “mistake.” New Series from Old 3 Series for rational functions using long division and geometric series New Series from Old 1 substitution (Be sure to look at example 3) Graphing Taylor Polynomials Graphing calculator hints Which Convergence Test Should I Use? Part 2 Specific hints and a discussion of the usefulness of absolute convergence Which Convergence Test Should I Use? Part 1 Pretty much anyone you want! Also, an introduction to the Completeness Axiom. (Suitable for pre-calculus as well as calculus)Ī Lesson on Sequences An investigation, which could be used as early as Algebra 1, showing how irrational numbers are the limit of a sequence of approximations. The suggested time for Unit 9 is about 17 – 18 BC classes of 40 – 50-minutes, this includes time for testing etc.Īmortization Using finite series to find your mortgage payment. Topic 10.15: Representing Functions as Power Series. Finding the power series of a function by, differentiation, integration, algebraic processes, substitution, or properties of geometric series. Students should memorize the Maclaurin series for, sin( x), cos( x), and e x. Topic 10.14: Finding the Taylor and Maclaurin Series of a Function. The interval may be different at the endpoints. Term-by-term differentiation and integration of a power series gives a series with the same center and radius of convergence. The Ratio Test is used almost exclusively to find the radius of convergence. Topic 10.13: Radius and Interval of Convergence of a Power Series. Topic 10.11: Finding Taylor Polynomial Approximations of a Function. Topic 10.10: Alternating Series Error Bound. Topics 10.10 – 10.12 Taylor Series and Error Bounds Absolute convergence implies conditional convergence. Topic 10.9: Determining Absolute and Conditional Convergence. Topic 10.7: Alternating Series Test for Convergence. Topic 10.6: Comparison Tests for Convergence. Comparison test and the Limit Comparison Test Harmonic series and alternating harmonic series, p-series. Topic 10.5: Harmonic Series and p-Series. Topic 10.4: Integral Test for Convergence. Topic 10.3: The n th Term Test for Divergence. However, teachers may include additional methods. The tests listed below are tested on the BC Calculus exam. 2: Working with Geometric Series. Including the formula for the sum of a convergent geometric series. Topic 10.1: Defining Convergent and Divergent Series. These topics account for about 17 – 18% of questions on the BC exam.