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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