Quiz #6 for Math 221
Instructions. Be sure to show your work and explain your reasoning for full credit.
1. A 160 F cup of coee is taken outside on a cool day of 55 F. After 10 minutes the
coee has cooled to 150 F. When will the coee cool to 110 F?
Soluti
The following are the questions used for the rst Exam in Math 221 section EL1
in Fall 2011 (McCarthys section). It is rather dierent than the one to be used in
sections AL1 and BL1 for Fall 2012 but it is being provided for those curious about
McCarthys e
Quiz #5
Math 221
Instructions. Be sure to show your work and explain your reasoning for full credit.
NAME
Find the derivative
dy
.
dx
1. y = sin1 (x3 )
Solution:
1
dy
=
3x2 .
6
dx
1x
2. y = ln(tan(ex )
Solution:
dy
1
=
sec2 (ex )ex .
dx
tan(ex )
3. y = xc
Math 221/AL1 Exam I
UIUC, September 27, 2013
Instructions. Please provide your answers in the space providedusing the back of
sheets if necessary. No calculators, electronics, friends or psychic readings are to be
used while taking this test. If you are u
The following are the questions used for a version of Exam I in Math 221 section
AL1 in Fall 2012 (McCarthys section). It may be rather dierent than the one to be
used in sections AL1 and BL1 for Fall 2013 but it is being provided for those curious
about
Solutions for Quiz #3
Math 221
Instructions. Be sure to show your work and explain your reasoning for full credit.
1. Determine the horizontal and vertical asymptotes to
3ex + 4
2ex 1
Solution: For the horizontal asymptotes,
ex (3 + 4ex )
3
3ex + 4
3ex +
Solutions for Quiz #2
Math 221
Instructions. Be sure to show your work and explain your reasoning for full credit.
1. Compute the limit
(2 + h)2 4
lim
h0
h
Solution:
(2 + h)2 4
4 + h2 + 4h 4
h2 + 4h
h(4 + h)
= lim
= lim
= lim
= 4.
h0
h0
h0
h0
h
h
h
h
lim
Solutions for Quiz #1
Math 221
Instructions. Be sure to show your work and explain your reasoning for full credit.
Solutions
1. Determine the point in the plane R2 where the line with slope 2 and y-intercept 1
intersects the line passing through the point
Math 213, Section X1
Midterm Exam 1
Spring 2006
Name:
Net-ID (or UIN):
Instructions
1. Rules. The usual rules apply: Closed books, notes, and no calculators.
2. Write-up of solutions. Except for multiple-choice problems (of which there are
two), an answer
Math 213, Section X1
Midterm Exam 1 Solutions and Comments
Spring 2006
Problem 1
Let A = cfw_0, 1 and B = cfw_2, 3. Write down the following sets, using proper mathematical
notation (e.g., use parentheses or braces as appropriate).
1. The power set of A:
Math 213 F1
Midterm Exam 1 Solutions
Prof. A.J. Hildebrand
Grading: The exam was worth 100 points. The breakdown per problem is given on the
coversheet. For multipart problems, each part was worth 5 points.
Exam statistics: Scores ranged from 39 to 100.
Math 213, Section X1
Midterm Exam 2 Solutions
Spring 2006
Problem 1
Suppose you roll 4 ordinary dice. Determine the following probabilities:
1. The probability that at least one 6 comes up.
Solution: By the complement trick, this is 1 P (no 6 in 4 rolls),
Math 213 F1
Midterm Exam 2 Solutions
Prof. A.J. Hildebrand
Grading notes
Exam statistics: The maximal score was 100 points; the median score was 70.
Score breakdown: The breakdown per problem is as follows: Problem 1: 30 pts (5 each); Problem
2: 15 pts
Math 213, Section X1
Midterm Exam 3 Solutions
Spring 2006
Problem 1
Consider 101 sets with the following properties: (i) each set has 1000 elements; (ii)
the intersection of any two distinct sets has 20 elements; (iii) the intersection of any
three pairwi
Math 213 F1
Midterm Exam 3 Solutions
Prof. A.J. Hildebrand
Grading notes
Exam statistics: The median score was 70, and the average 69. This is similar to the score
statistics on the earlier midterms.
Score breakdown: The breakdown per problem is as foll
Name:
Collaborator(s)1 :
Math 213, Section F1, Prof. Hildebrand, Fall 2010
Graded HW Assignment 1, due Friday, 9/3/2010
Instructions
Use this sheet as cover sheet and staple it to the assignment. Do the problems in order,
and make sure that each problem
Name:
Collaborator(s)1 :
Math 213, Section F1, Prof. Hildebrand, Fall 2010
Graded HW Assignment 2, due Friday, 9/10/2010
Instructions
Use this sheet as cover sheet and staple it to the assignment. Do the problems in order,
and make sure that each problem
Name:
Collaborator(s)1 :
Math 213, Section F1, Prof. Hildebrand, Fall 2010
Graded HW Assignment 6, due Friday, 10/22/2010
Instructions
Rules: Use this sheet as cover sheet and staple it to the assignment. Do the problems in
order, and make sure that each
Math 213
Worksheet: Induction Proofs III, Sample Proofs
A.J. Hildebrand
Sample Induction Proofs
Below are model solutions to some of the practice problems on the induction worksheets. The solutions given
illustrate all of the main types of induction situa