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Topics for Calculus 2 Exam

posted May 21, 2018, 9:34 AM by Matthew Grenfell   [ updated May 14, 2019, 4:23 AM ]
  • Numerical Integration.
  • Solving separable differential equations.
  • Finding a Taylor polynomial of a function. 
  • Using Taylor’s inequality when bounding the accuracy of a Taylor Polynomial over a closed interval.
  • Integration by parts.
  • Trigonometric substitution.
  • Improper integrals.
  • Determining conditions for a series to converge.
  • Using he comparison or limit comparison test to determine convergence.
  • Determining conditional or absolute convergence.
  • Being able to recognize a p-series and use it to help determine convergence.
  • Being able to use a root or ratio test to determine convergence.
  • Finding the radius of convergence.
  • Finding the interval of convergence.
  • Using Taylor or Maclauren series when integrating functions that can’t be antidifferentiated.
  • Finding the tangent line to a curve given parametrically at a specific point.
  • Finding the polar coordinates for points of intersection of two polar curves.

  • Recognize a geometric series and to what it converges
  • Arc length of a curve
  • Partial Fraction decomposition of a rational function.
  • Determining the convergence or divergence of a series using various tests.  
  • Understanding when a particular convergence test can be applied
  • Conversion from Cartesian coordinates to polar coordinates and vice versa.
  • Writing the rectangular form of a polar curve.
  • Understanding the application of alternating series when minimizing the degree of a polynomial to approximate a series to within a certain value. 
  • Using known series to find series of other functions; e.g., Find the Maclaurin series of 1/(1-x^3), or of 
  • ln((1-x)/(1+x)) or ...
  • More integrals requiring advanced techniques of integration.
  • Using Taylor’s inequality to find the smallest degree of the Taylor polynomial which will give an estimate within an error of some small value. The Taylor remainder term inequality will be supplied. 
  • Finding the integral which calculates the work done in stretching a spring a certain distance beyond its natural length. 
  • Finding the integral which calculates the work done in pumping water out of a tank.
  • Finding the integral of the area inside one polar curve and outside another polar curve.