MATH 1451 Exam 3

Our third exam will be Fri, Apr 13 in class.
The exam will cover material since the second exam.
In particular, this is sections 9.1, 9.2, 9.3, 9.4,
9.5, 10.1, 10.2, and 10.3.

There will NOT be questions on Error Bounds for Alternating
Series. 

Remember that one of the best ways to prepare for the test
is to work on practice problems.  These might include
problems from the Suggested Study Problems (on the class
website), odd-numbered problems from text (which have
answers available on WileyPLUS in the "Read, Study &
Practice" section), problems in the WileyPLUS assignments.
Don't just read the problems and solutions - copy the problem
to a new sheet of paper and try to work out the answer
yourself.

To help organize your studying, I've listed some of the
major topics from this material:

- Sequences: recursive definitions, formulas, convergence

- Convergence of a monotone, bounded sequence

- Sum of finite geometric series

- Sum of infinite geometric series

- Partial sums and convergence of infinite series

- Convergence properties of series

- Harmonic series and alternating harmonic series

- The Integral Test for series convergence

- The Comparison Test for series convergence

- The Limit Comparison Test for series convergence

- The Ratio Test for series convergence

- The Alternating Series Test for series convergence

- Deciding if a series is absolutely convergent or if it is
   conditionally convergent

- Definition of a power series about x = a

- Finding the Radius of Convergence for a power series

- Finding the Interval of Convergence for a power series

- Computing the Taylor Polynomial of degree n approximating
   f(x) about x = a

- Computing the Taylor Series for f(x) about x = a

- Know and recognize the Taylor Series about x = 0 for sin x,
   cos x, and e^x

- The Binomial Series for (1 + x)^p

- Computing new Taylor Series from old by: substitution,
   differentiation, integration, multiplying