Exam III will be held in the usual room at the usual time: 12:30-1:20 on Friday Apr. 20. It will start promptly at 12:30, so make sure you're on time. The test will cover sections 6.6 - 7.5. Note that we did not cover Cauchy's Mean Value Theorem from section 6.8.

The test will have four problems, possibly with several parts each. Calculators or other mechanical assistance are not needed and are not to be used.

update: you may bring a 4x6 card with notes on it.

The sections covered on this exam contained a lot of definitions and formulas to remember. Some of these are more important than others. Please do learn:

• the definitions (including domain and range, etc) for arcsin, arccos, and arctan
• the derivatives of arcsin, arccos, and arctan, and the corresponding integration formulas
• the definitions of hyperbolic sine, cosine, and tangent
• the derivatives of hyperbolic sine, cosine, and tangent
• the definitions (including domain and range, etc) of inverse hyperbolic sine, cosine, tangent
• the derivatives of inverse hyperbolic sine, cosine, and tangent
• the antiderivatives of tan x and sec x

• domain, range, etc for inverse cosecant, inverse secant, inverse cotangent
• derivatives of inverse cosecant, inverse secant, inverse cotangent
• the alternative formulas for the inverse hyperbolic trig functions (in terms of ln)
• hyperbolic trig identities

In addition to the items listed earlier, the exam may also include (but is not limited to):

• composing a trig function with an inverse trig function
• limits and L'Hospital's rule
• integration by parts
• integrating products of powers of trig functions, using trig identities
• integration of rational functions using partial fractions:
  • using long division to deal with rational functions that are not proper
  • writing the correct form of the partial fraction expansion of a proper rational function, based on the factors of the denominator
  • solving for the constants
  • integrating the resulting terms, which will be (constant)/(linear) or (linear)/(quadratic)

Advice:

• Read and review section 7.5. Also look at the "Concept Check" questions at the end of Chapters 6 and 7 to find out which conceptual areas need review.
• Learn what the "routine" problems are, and practice so that you can do them quickly and easily. Remember, they always seem harder in an exam situation, so practice and build your confidence.
• You may need to brush up on computing derivatives and integrals (eg. chain rule, substitution, etc).

When it comes time for the test itself, relax and do the best you can. Because you have studied, you know which topics you know best, and can get those problems out of the way quickly. Then you'll have time to spend on the remaining ones.