Math402/Advanced Calculus I Test Study Guide
----Test # 2-----
Second Test:Thursday, November 12, 1998
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....General Information About The Exam....
....(this information is the same as it was for Test #1)....
....(check the test #1 test guide page for details )....
A FEW IMPORTANT REMINDERS!
The test will be worth 80 points and will
constitute roughly 25% of the total number of test points
for the course.
You will have 1hr and 20min to work on the test.
All of your work must be placed in the "Blue Book(s)"
that will be provided for you.
The answers in the Blue Book(s) must appear in the same order
as they appear on the test sheet, and so you will need to
plan ahead and leave necessary space if you intend to
work the problems out of order.
....Specific Information About The Exam....
0. Know how to work any assigned homework problem
(from section 3.1 through 4.4)
1. Be able to state and prove the Monotone Convergence Theorem
2. Be able to state and prove the Bolzano-Weierstrass Theorem
3. Be able to state and prove the Nested Interval Theorem
4. Define Continuity at a point (pg43)
5. Know how to prove that the sum, difference, product, quotient
and composition of continuous functions is continuous
(under necessary assumptions)
6. Be able to state the Extreme Value Theorem (pg 47)
7. Be able to prove the Intermediate Value Theorem ie th 3.8 (assuming Th 3.7 pg 49)
8. Be able to define Uniform Continuity (pg 58)
9. Be able to prove uniform continuity implies continuity
10. Be able to prove that continuous functions defined on closed
intervals are uniformly continuous.
11. Be able to define a limit point of a set
12. Be able to define the limit of a function
13. Be able to prove that if f and g are functions that have limits at x0,
the the sum, difference, product and quotient have limits at x0. Also,
if f has a limit at x0, say y0 and g has a limit at y0 then gof has
a limit at x0 (under necessary assumptions)
14. Be able to define the derivative of a function
15. Be able to prove that if f and g are functions that are
differentiable at x0, then the the sum, difference, product
and quotient are differentiable at x0. Also, if f is differentiable
at x0, and g is differentiable at f(x0) then gof is
a differentiable at x0 (under necessary assumptions)
16. Know the formula for the derivative of the inverse of a
function (no proof)
17. Be able to prove Rolle's Theorem ie th 4.13
18. Be able to prove The (Lagrange) Mean Value Theorem ie th 4.14
(last updated 6:00AM on 11-4-98)