Math 3310 Theoretical Concepts of Calculus
Solutions to Review Problems for
Quiz 1, Wednesday, 1/23
Section 1 : Exercises 1:3; 1:4; 1:7 1:10; 1:13; 1:14.
Exercise 1:3 Write the negation of each statement.
a) M is a cyclic group
Negation: M is not a cyclic
Math 3310 Theoretical Concepts of Calculus
Spring 2014
Solutions to Review Problems for Quiz 1
by Dr. M.Dabkowska
Section 1.1 : Exercises 3; 4; 7 10; 13; 14.
Exercise 3 Write the negation of each statement.
a) The 3
3 identity matrix is singular.
Negation
Math 2510: Real Analysis I Homework Solutions 1
Fall 2008
1 Logical Connectives
1.4 Write the negation of each statement. (b) The set of rational numbers is bounded. Negation: The set of rational numbers is unbounded. (c) The function f is injective and s
Math 3310 Theoretical Concepts of Calculus
Quiz 5 Review
Section 5.3
We will use the intermediate value theorem in the following problems.
Exercises 4 : Show that 3x = 5x for some x 2 (0; 1).
Solution: Let f (x) = 3x 5x: Notice
3x = 5x has a solution insi
Math 3310 Theoretical Concepts of Calculus
Homework 1
Due: Wednesday, 1/20/2015
Name
Instructions. Please solve the following problems (show all your work ). You can use your textbooks,
class notes, and material posted on eLearning. Do not discuss the pro
Math 3310 Theoretical Concepts of Calculus
Homework 4
Due: Wednesday, 3/23/2016
Name
Instructions. Please solve the following problems (show all your work ). You can use your textbooks,
class notes, and material posted on eLearning. Do not discuss the pro
Page 180 Problem 3bd
Prove that each sequence is monotone and bounded. Then find the limit.
1
(b) s1 = 2 and sn+1 =
4 (sn + 5) for n N.
(d) s1 = 2 and sn+1 = 2sn + 1 for n N.
Solution
(b) We first show that |sn | < 3 for all
1 | = 2is less than 3. Suppos
MATH 3310.002, Theoretical Concepts of Calculus
Times and Location: MW, 11:30am-12:45pm, CB3 1.312
Instructor: Dr. Malgorzata Dabkowska
O ce: Founders Building 2.604C
O ce hours: MTWR, 1:00-2:00pm, or by appointment
E-mail: [email protected]
Phone: (972)
Math 3310 Theoretical Concepts of Calculus
Review problems and solutions for Exam 1
Section 1.1
Exercise 3 Write the negation of each statement.
a. The 3
3 identity matrix is singular.
Negation: The 3
3 identity matrix is not singular.
b. The function f (
Math 3310 Theoretical Concepts of Calculus
Homework 2
Due: Wednesday, 2/3/2016
Name
Instructions. Please solve the following problems (show all your work ). You can use your textbooks,
class notes, and material posted on eLearning. Do not discuss the prob
Math 3310 Theoretical Concepts of Calculus
Homework 3
Due: Wednesday, 3/2/2016
Name
Instructions. Please solve the following problems (show all your work ). You can use your textbooks,
class notes, and material posted on eLearning. Do not discuss the prob
Math 3310 Theoretical Concepts of Calculus
Solutions to Review Problems for Quiz 1
Section 1.1
Exercise 3 Write the negation of each statement.
a) The 3
3 identity matrix is singular.
Negation: The 3
3 identity matrix is not singular.
b) The function f (x
Math 3310 Theoretical Concepts of Calculus
Solutions to Review Problems for Quiz 2
Section 2.2
Exercise 11 Determine which properties apply to relations:
a. Let R be the relation on N given by xRy i xjy.
The relation R is reexive b/c
8x2N (xjx);
However,
Math 3310 Theoretical Concepts of Calculus
Review Problems for Quiz 3
Section 3.3
Exercises 3 and 4: For each subset of R; give its supremum and maximum, inmum and minimum, if
they exist. Otherwise, write "none".
a) f1; 3g
Clearly, we have: sup f1; 3g = 3
Math 3310 Theoretical Concepts of Calculus
Quiz 4 Review
Section 4.2
Exercise 5: For sn given by the following formulas, determine the convergence or divergence of the
sequence (sn ) : Find any limits that exist.
a. sn =
3 2n
1+n
Solution: The sequence (s
Math 3310 Theoretical Concepts of Calculus
Solutions to review problems for Exam 2
Section 3.3
Exercises 3 and 4: For each subset of R, give its supremum and maximum, inmum and minimum, if they
exist. Otherwise, write "none".
a. f1; 3g
Solution: Clearly,
Math 3310 Theoretical Concepts of Calculus
Solutions to selected review problems for Exam 2
Exam 2: Tuesday, 4/8/14
Section 3.3
Exercises 3 and 4: For each subset of R; give its supremum and maximum, inmum and minimum, if they
exist. Otherwise, write "non
Math 3310 Theoretical Concepts of Calculus
Solutions to Quiz 5 Review
Section 5.4
Exercise 3: Determine which of the following continuous functions are uniformly continuous on the
given set. Justify your answer.
(a) f (x) =
ex
x
on [2; 5]
Solution: Since
Math 3310 Theoretical Concepts of Calculus
Solutions to selected review problems for
Exam 1: Wednesday, 2/20/2013
Section 1 :
Exercise 1:9 Indicate whether each statement is True or False.
a) 2
3 and 7 is prime
Both sentences: "2 3" and "7 is prime" are T
Math 3310 Theoretical Concepts of Calculus
Solutions to Quiz 5 Review
Exercise 26:5 : Use the Mean Value Theorem to establish the following inequalities:
(a) ex > 1 + x; for x > 0:
Solution: Let f (t) = et ; where c 2 [0; x]: Since f is continuous on [0;
Math 3310 Theoretical Concepts of Calculus
Solutions to selected problems for Quiz 4 review
Exercise 16:6: Using the Denition 16:2, prove that:
(a) For any real number k
lim
n!1
k
n
=0
Solution: Let > 0 be given. We need to nd N0 2 N; such that, for n > N
Math 3310 Theoretical Concepts of Calculus
Solutions to Selected Review Problems for Quiz 3
Section 13 : Exercises 13:3
13:6.
Exercise 13:3 Find the interior of each set.
a)
1
n
: n2N
Solution: We see that int
1
n
: n2N
= ; because for any x 2 R and
N (x;
Math 3310 Theoretical Concepts of Calculus
Solutions to Selected Review Problems for Quiz 2
Section 5 : Exercises 5:3; 5:4; 5:5; 5:6; 5:7; 5:8; 5:9; 5:10; 5:11; 5:25.
Exercise 5:3 Let A = f2; 4; 6; 8g; B = f3; 4; 5; 6g; and C = f4; 5g: Which of the follow
Math 3310 Theoretical Concepts of Calculus
Solutions to selected review problems for Exam 2
Exam 2: Wednesday, 4/10/2013
Section 13
Exercise 13:3 Find the interior of each set.
a)
1
n
: n2N
Solution: We see that int
1
n
: n2N
= ; because for any x 2 R and
Practice Problems Ch 3 : Dr. Avanti Sethi
From the book: #10, 16, 24, 28, 32, 40, 52, 54, 58
Extra Problems
Consider this set of data: 2, 3, 1, 4, 1, 3, 2, 4
1. What is the mean?
2. If the dataset represents a population, what is the variance? Standard de
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Math 3310 Theoretical Concepts of Calculus
Solutions to selected review problems for Exam 1
by Dr. M.Dabkowska
Section 1.1 : Exercises 3; 4; 7 10; 13; 14.
Exercise 3 Write the negation of each statement.
a) The 3
3 identity matrix is singular.
Negation: T
Math 3310 Theoretical Concepts of Calculus
Homework 1
Due: Thursday, 1/30/2014
Name
Instructions. Please solve the following problems (show all your work ). You can use your textbooks,
class notes, and material posted on eLearning. Do not discuss the prob
Math 3310 Theoretical Concepts of Calculus
Homework 2
Due: Thursday, 2/13/2014
Name
Instructions. Please solve the following problems (show all your work ). You can use your textbooks,
class notes, and material posted on eLearning. Do not discuss the prob