Mathematics 36, section 1 -- AP Analysis

Information on Exam 2

October 24, 1997

General Information

The second exam for the course will be given next Friday, October 31, as announced in the course syllabus. It will cover the material discussed in class since the first exam through and including Friday October 24. The topics are:

  1. Taylor polynomials, approximations, the error bound
  2. Taylor series,
  3. Total change of a function, Riemann sums, the definite integral,
  4. The Fundamental Theorem of Calculus, and
  5. Integration by substitution and by parts
The format will be similar to that of the first exam.

Review Session

To help you review and prepare for the exam, if there is interest, we can schedule an evening review session next week. Is Wednesday good?

Suggested Practice Problems

From the text: p. 650-1/ 1-4 (don't work harder than you have to!), 11 (use Taylor polynomials)

p. 337-9/ 1-3, 5-9, problems like 10-33, 40

p. 415/9, 10, 11, 12, 15, 16, 18, 19, 21 and definite integrals like these.

p. 181-2/8, 10, 12

Additional problems

Give a bound on the size of the error if we approximate sqrt(2) using the Taylor polynomial of degree 3 for f(x) = sqrt(1+x), a = 0. Compute the approximation, and compare with a calculator sqrt key value for sqrt(2).

Using the error bound, determine what degree Taylor polynomial for f(x) = sin(x), a = 0, is needed to compute sin(2) to 4 decimal place accuracy. Compute the approximation, and check against a calculator value.

Practice Exam

Here is last year's Exam 2 to practice on.