Solutions to Homework 1
Due Friday, June 25, 2004.
Chapter 1.1.
Problem 1 solution. If is an even linear function then must be constant. If z (w, 1) = z (w, 1) = 0 then (w) (1) = (w) (1) = 0. The
rst
Solutions to Homework 2
Due Tuesday, July 6, 2004.
Chapter 2.3
Problem 3 solution. If the series for ln(1+z ) and ln(1z ) both converge,
1+
then we can nd the series for ln 1z by term-by-term subtract
Solutions to Homework 3
Due Tuesday, July 13, 2004.
Chapter 3.1
Solution to problem 1. Less than 0.001: k = 11 works. Less than
0.000001: k = 15 works. (Note. I dont know why the author wants
to use S
Solutions to Homework 4
Due Tuesday, July 20, 2004.
Chapter 3.3) 1, 2, 7, 9, 17, 19.
Solution to problem 1. Cauchys proof requires that i) f is dierentiable
at every point in [a, b] ii) f is bounded o
Solutions to Homework 5
Due Tuesday, July 27, 2004.
Chapter 3.4) 2, 3, 5, 10, 11, 14, 15, 22, 23, 26.
Solution to problem 2. Here is a graph:
0.1
0.08
0.06
0.04
0.02
-0.1
-0.05
0.05
0.1
It looks like
Solutions to Homework 6
Due Friday, July 30, 2004.
Chapter 3.5) 3, 4, 5, 7, 8, 9, 16.
Solution to problem 3.
a.
b.
c.
d.
e.
l.u.b. = 3, g.l.b = 0.
l.u.b. = 1, g.l.b. = 0.
(note 1 + 1/2 + 1/4 + 1/8 + =
Solutions to Homework 7
Due Wednesday, August 4, 2004.
Chapter 4.1) 3, 4, 9, 20, 27, 30. Chapter 4.2) 4, 9, 10, 11, 12.
Chapter 4.1.
Solution to problem 3. The sum has the form
a1 a2 + a3
with ak = 1
Solutions to Homework 8
Due Friday, August 6, 2004.
Chapter 4.3) 1f, 7f.
n+1
Solution to problem 1f. Its easy to see that | aan | =
a rational function of n.
(2n+1)2
(n+1)2
which is
Solution to proble
Solutions to Homework 9
Due Friday, August 13, 2004.
Chapter
Chapter
Chapter
Chapter
4.4)
4.5)
5.1)
5.2)
3
9, 12
2, 3, 10, 11
4, 5.
Chapter 4.4.
Solution to problem 3. Let f (x) = x(ln 1 )3/2 . It is
Math 650 Summer 2004 Test 1. Wednesday, July 7, 2004
Name:
1. Fouriers series for a function equal to 1 on the interval (1, 1) is given by
f (x) =
4
x 1
3x 1
5x 1
7x
cos
cos
+ cos
cos
+ .
2
3
2
5
2
Topics to Review for Test 2
Chapter 3.1. Newton-Raphson method. Conditions that guarantee convergence.
3.2. Dierentiability. Why derivatives of innite sums may not be the
2
sum of the derivatives. Str
Math 650 Summer 2004 Test 2 Solutions. Friday, August 6, 2004.
Name:
1. Use the Mean Value Theorem to prove that if f is continuous on [a, b],
dierentiable on (a, b) and f (x) > 0 for all x in (a, b),
Math 148 Test 1 Version A Solutions Autumn 2002
Name:
Instructor and class time:
This is the solutions to version A of the rst midterms.
h
1. (10 pts) Solve A = (b + c) for b
2
2A
c = b. Note: other
Notes for Math 148, Wed., Oct. 2
Homework questions:
1:002:05 p.m. class: A question was asked about #53 in section 1.1. The problem is easy because the
square has sides parallel to the coordinate axe
Math 148 Quiz 1a Autumn 2002
Name:
Class time (circle one):
1:00 p.m.
2:30 p.m.
Please read all the questions carefully and show your work. Credit may not be awarded if answers are not
supported by wo
Math 148 Quiz 2a Solutions Autumn 2002
1. Let f (x) = 2x + 1. Find f (3 + 1).
Answer: f (3 + 1) = f (4) = 9.
2. A parabola has vertex at the point (5, 6) and a zeros at x = 7 and x = 3. Find the equat
Solutions to problems from old Math 148 Final Exams
1. x = 4/3
2. a) f (2) = 8, f (x) = x4 x3 7x2 + 12
b) z = 2, 3
3. $236.20
4. Dimensions of sheet are 20 by 15 feet (dimensions of the box itself are
Problems from old Math 148 Final Exams
These problems can be downloaded from the course home page:
http:/www.math.ohio-state.edu/courses/math148/
1. Solve x2 3x + 4 = x
2. Let f (z ) = z 4 + z 3 7z 2