MAC 3473 Honors Calculus II (Review for Exam 2)

• 7.7 Improper Integrals
• Be able to explain if an integral is improper determine whether it converges and find its value.
• State the Comparison Property.
• Determine whether an improper integral converges using the Comparison Property.
• Chapter 8: Applications of the definite integral.
• Understand and recognize how some physical quatity can be approximated in terms of Riemann sums and written in terms of a definite integral.
• 8.1 Volume: cross-sectional method.
• Find the volume of a solid using the cross-sectional method and write up the solution in a proper and coherent manner.
• Disk Method.
• Washer Method.
• 8.2 Volume: The Shell Method.
• 8.3 Length of a curve.
• 8.5 Work
• Definition of work done by a force acting on moving and object along a straight line.
• Writing up a work problem and determing the relevant definite integral.
• Pool problems.
• 9.1 Polynomial approximations
• Finding Taylor polynomials
• Finding the n-th Taylor polynomial
• Using a Taylor polynomial to find an approximation to f(x).
• 9.2 Sequences
• Define what it means for L to be the limit of a given sequence.
• Proving the value of a limit using the formal definition.
• Calculating limits of sequences.
• 9.3 Convergence Properties of Sequences
• State the Squeezing Theorem.
• Calculating limits using the Squeezing Theorem.
• Calculating more limits.
F.G. Garvan/frank@math.ufl.edu/October 31, 1995 (created 10/31/95)

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