Midterm Review One (Partial) Solutions
Instructor: M. Tychonievich
Math 1161, Autumn 2012
1. (18 Points) Find the following limits:
a)
(2 + 2h)4 16
h0
h
lim
Set f (x) := (2 + 2x)4 . Then f (0) = 16, s
Calculus for Scientists and Engineers: Multivariable
By Briggs, Cochran, Gillett
First Printing Errata List
Chapter 13
p. 895, In the first line of Section 13.2, Chapter 11 should read Chapter 12.
p.
Math 2162.01 & 02
Accelerated Calculus II
Name:
name.#:
Recitation Instructor:
Recitation Time:
W RITTEN H OMEWORK 3
Directions:
Show your work. Your solution should be easily understood by someone w
Math 2162.02 Midterm 3 Review Problems
Our third midterm will be held on Monday, April 11 in class. It will cover all that weve
done in Chapters 13.7 through 15.4. There will be approximately six ques
Math 2162.01 & 02
Accelerated Calculus II
Name:
name.#:
Recitation Instructor:
Recitation Time:
N OT-H OMEWORK S TAND - IN FOR W RITTEN H OMEWORK 5
Directions:
Below are a few interesting examples an
Math 2162.01 & 02
Accelerated Calculus II
Name:
name.#:
Recitation Instructor:
Recitation Time:
W RITTEN H OMEWORK 4
Directions:
Show your work. Your solution should be easily understood by someone w
MIDTERM 1 SOLUTIONS
Question 1. (11 points)
i) (7 points) Let f (x) = 2 2 cos(tan(x) x. Find the value of the real number a if: a = 2f 0 (0) + 1.
Sol. Using the chain rule, we have: f 0 (x) = 2 2 sin(
APPLICATION OF ROLLES THEOREM-SOLUTIONS
Problem 1. Show that the equation:
(a) 4ax3 + 3bx2 + 2cx = a + b + c has at least one root on (0, 1).
Sol. Let F (x) = ax4 + bx3 + cx2 (a + b + c)x, for x on [0
APPLICATION OF MEAN VALUE THEOREM
Problem 0.1. Show that f (x) = 2x + sin x 5 has at most one solution.
Proof. We prove this by contradiction. Assume that f (x) has more than one solutions, and suppos
Practice Midterm 1 Math 1161.0X
1. Decide if the following statements are TRUE or FALSE. You do NOT need to justify your answers.
(a) (1 point) If f and g are differentiable at a then f g is different
Midterm Review One
Name:
Instructor: C. Ross
Math 1161, Autumn 2012
48-minute exam
All work must be shown to receive maximum points. Justify your responses; answers
without supporting work will receiv
Math 1161, Autumn 2012
Dr. C. Ross
Personal Information
Email: [email protected]
Oce: Math Tower (MW) 349
Hours: Tuesday & Thursday at 12:00-1:30 (tentative), and by appointment
Course Informa
Here is a solution to the bonus problem on the sample nal. Please remember that as
a bonus problem, it is not only worth fewer points than a standard problem, but it is also
much more dicult than a st
Math 1161, Autumn 2012
Michael A. Tychonievich
Personal Information
Email: [email protected]
Oce: Math Tower (MW) 629
Hours: Monday, Wednesday, and Friday 12:30PM 1:30PM, and by appointment
Co
Final Review
Read textbook and class notes. Refer to the book or class notes if you forget any
concept or formula.
1. Limits
1) Techniques for computing limits
1) Using continuity and limit laws: (Wha
Final Exam Review
Name:
Instructors: Ross, Tychonievich
Math 1161, Autumn 2012
Exam duration: 1.8 hours
All work must be shown to receive maximum points. Justify your responses; answers
without suppor
FIRST DAY OF CLASS
Registration Instructions
Access Code
Before you get started, be sure
you have your MyMathLab
access code.
If you are purchasing a paper textbook, this
access code will come with th
math 1161 AU12
Math 1161.01=Math1161.02: Autumn Syllabus and Calendar: 5 credit hours
Textbook = Calculus forScientists and Engineers by William Briggs
Warning: Although Briggs' motivation for the dif
Midterm Review One
Name:
Math 1161, Autumn 2012
55-minute sample exam
All work must be shown to receive full credit. Justify your responses; answers without
supporting work receive no credit.
Exact an
Midterm Review Three
Name:
Instructors: Ross, Tychonievich
Math 1161, Autumn 2012
48-minute exam
All work must be shown to receive maximum points. Justify your responses; answers
without supporting wo
Midterm Review Two
Name:
Instructors: Ross, Tychonievich
Math 1161, Autumn 2012
48-minute exam
All work must be shown to receive maximum points. Justify your responses; answers
without supporting work
Midterm Review Two
Hints and Partial Solutions
Math 1161, Autumn 2012
1. (20 Points) Find the following limits:
a)
1
n n3
2n
(k + 1)(k 1)
lim
k=1
You can evaluate this using summation formulas, or not