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### 2018/2019 - Topics for the Calculus 2 Final Exam

posted May 14, 2019, 4:20 AM by Matthew Grenfell   [ updated May 14, 2019, 5:15 AM ]
 Use integration by parts to evaluate integrals Evaluate trigonometric integrals (e.g., integrate sin^3(x), sec^2(x)tan^2(x), and so on) Evaluate integrals by making trig substitutions Evaluate integrals using partial fractions Determine the convergence/divergence of improper integrals and evaluate if convergent Use various tests to determine the convergence/divergence of series, including the integral test, comparison tests, and ratio test Determine the convergence/divergence of a geometric series or alternating series Determine a power series representation of a given function Determine the radius of convergence and interval of convergence for a power series Determine a Maclaurin or Taylor series representation of a function Determine a Taylor polynomial of a certain degree for a given function Determine the solution of a separable differential equation Graph curves defined by parametric equations Determine the derivative at a point on a parametric curve Describe and work with points and curves in polar coordinates Determine areas of common regions using polar coordinates More integration by parts Approximate integration techniques (Midpoint Rule, Trapezoidal Rule, Simpson's Rule) Sequences More power series/Taylor series (preferably deriving a Taylor series from scratch) Approximating error of an integration technique or Taylor polynomial Work (draining a tank, for example) More on parametric curves and calculus with parametric equations