Final Exam study guide
- The final exam is comprehensive with an emphasis on Sections
4.1-3, 4.5, 4.6, 5.1-2 as well as the Evaluation Theorem.
- The final will have approximately 10 questions, with the
usual mix of True-False, stating of key definitions and theorems,
as well as word problems and computational problems.
- There may be some multiple choice questions as well.
- About half of the questions will be on material we covered
since exam 2. Consult the schedule
for material which we covered.
- This course has had 3 important themes:
- Limits:
- The concept of a limit.
- The limit laws.
- Continuity.
- Differentiating functions:
- The definition of the derivative as a limit.
- Basic derivatives of polynomial,
rational, trigonometric, inverse trigonometric,
exponential and logarithmic functions.
- Power, sum, difference, product, quotient and chain rules.
- Implicit and logarithmic differentiation.
- Applications of derivatives:
- Related rates problems.
- Sketching a function. This includes determining features
like domain, range, local extrema, continuity, intervals of
increase and decrease,
horizontal and vertical asymptotes.
- Optimization.
- Displacement, velocity, speed, acceleration.
- One subject were all these themes meet is L'Hopital's rule.
- Another one is sketching a function. This requires determining
features like domain, continuity, local extrema, intervals of
increase and decrease, inflection points, horizontal and vertical
asymptotes.
- You should still remember the basic material from Chapter 1.
(Hopefully this is second nature by now.)
- You should be familiar with all the terminology we are using,
like increasing, inverse function, composition, continuity, difference
quotient...
- I recommend the Review questions on pages 84 (#1-12), 181
(#1-15), pg 258 (#1-4), pg 336 (#1-8, 10a) and pg 438 (#1-3a).
If there are questions that you find hard to answer,
then I strongly recommend rereading the corresponding material, since
there will be a question of this type on the exam!
- Review your lecture notes and your homework, they are your friends.
- I suggest doing as many problems from the chapter reviews
as you can (at least one problem from chapter 4 and/or 5 review
will be on the exam). Work on those that are in sections you know you
had difficulties with or which you simply don't remember anymore.
- Here is a list of problems that is particularly valuable.
If you have done these review problems
already, then picking odd numbered problems from the section itself
is good too.
- Chapter 2 (page 182-184) focus on 1, 3-16, 20-24, 27-28b), 32-34,
37,38,42,46.
- Chapter 3 (page 259-260) focus on 1-31,41-48,51-56d).
- Chapter 4 (page 337-339) focus on 1-12,25-30,33-38,41,42,59.
- Chapter 5 (page 439-440) focus on 1,3-5,7,9-16,19.
- If you have the time for it, then doing extra problems
from the book is the way to go in any Math class.
The more you work with the concepts, the "readier" you are going to be.
- Some problems on the exam may throw you off at first.
Make sure that you get a good nights sleep, so that you are fresh,
rested and ready to go!