Math 275 - Fall 2012
October 10, 2012, 19:15-20:45
First Midterm Exam Solutions
1. (15 pts) Decide for each of the following statements if they are true or not. If yes, give a
short proof why. If not, give a counterexample.
(a) The sum of two rational num
Hw 7, due next week in the discussion section.
Reading assignment: pp. 117130.
p. 114, problems 5,6,9,11.
p. 119, problems 9,10.
p. 124, problems 6,13.
1
The sample problems for the second Midterm
The second midterm will cover the material on pp. 88155 from the textbook.
There will be 4 or 5 problems.
1. Compute the area of the region between the graphs of f and g over the
interval [a, b]. Draw a sketch of
Final, the third part
The nal exam will be cumulative: some problems will be similar to the ones in
the rst and the second midterms. The rest will refer to the material covered after
the second midterm. The sample problems are
1. For f (x) = cos(3x), nd
f
Hw 1, due next week in the discussion section.
1. Prove that the equation x2 = 3 has no rational solutions.
2
2. Find a decimal decomposition of the rational number .
3
3. Find the fractional representation of the number that has the following
decimal rep
Math 275, Topics in Calculus I
Fall 2013
Basic Information
Instructor:
Oce:
Oce Phone:
E-Mail:
Web Page:
Texts:
Serguei Denissov
623 Van Vleck Hall
(608) 263-5564
denissov@math.wisc.edu
http:/www.math.wisc.edu/denissov
Calculus Vol. 1, Second edition, by
Hw 2, due next week in the discussion section.
1. Prove that
n
k=1
for every n N.
2. Prove that
n
k2 =
n3
n2
n
+
+
3
2
6
k 3 = (1 + 2 + . . . + n)2
k=1
for every n N.
3. The Fibonacci sequence is the sequence of numbers obtained through iterating the foll
Math 275 - Fall 2012
November 14, 2012, 19:15-20:45
Second Midterm Exam - Solution
1. (a) Give the precise denition of the upper and lower integral of a function f on an
interval [a, b].
The lower integral is dened as
b
s(x)dx s(x) f (x), for all x (a, b)
Innite limits, limits at innity
Math 275 Fall 2012
As we discussed in class, we can dene innite limits and limits at innity just by dening
the neighborhoods of and . The neighborhoods of are the intervals of the form
(c, ) and the neighborhoods of are the
MATH 275 Review sheet for the rst midterm exam
Time: Wednesday, October 10, 7:15PM-8:45PM,
Place: Social Sciences 6102 (NOTE THAT THIS IS NOT OUR USUAL CLASSROOM!)
This is an outline to help you study for the midterm exam. It is meant to give you a sample
MATH 275 Review sheet for the second midterm exam
Time: Wednesday, November 14, 7:15PM-8:45PM,
Place: Social Sciences 6102 (NOTE THAT THIS IS NOT OUR USUAL CLASSROOM!)
This is an outline to help you study for the midterm exam. It is meant to give you a sa
MATH 275 Review sheet for the nal exam
Time: December 18, Tuesday, 12:25PM - 2:25PM
Place: Ingraham 120
This is an outline to help you study for the nal exam. It is meant to give you a sample
of problems, concepts, topics you may encounter on the exam. No
Hw 3, due next week in the discussion section.
Reading assignment: pp. 2325, 2728, 5052, 5463.
p. 46, problems 14,16,17,22.
Let A and B be two bounded sets of positive real numbers. Consider
the set of all products, i.e., C = cfw_x y, x A, y B . Is C bo
Hw 4, due next week in the discussion section.
Reading assignment: pp. 6079.
pp. 7072, problems 5(b), 10(b).
The function f (x) dened on [a, a] is called odd if
f (x) = f (x)
for every x [a, a] and the function f (x) is called even if
f (x) = f (x)
Supp
Midterm 1 preparation kit
The midterm will be in class and there will be 4 or 5 problems. You can not use
books, calculators, or your notes. Collaboration is not allowed. You will need to
write up the solutions neatly and give the adequate explanations. T