Exam (elaborations)
MATH 100 Fall 2016 midterm exam with solutions
- Course
- Institution
- Book
MATH 100 Fall 2016 midterm exam with solutions
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
More summaries for
-
Multivariable Calculus Notes: Partial Derivatives
-
MAT1512 ASSIGNMENT 2 2023 SOLUTIONS
-
AP Calculus Review: U1 Limits and Continuity
Seller
Follow
xuyian222
Content preview
MATH 100—Midterm Examinationversion 1
Date: October 28, 2016 Time: 90 minutes
Surname: Given name(s):
(Please, print!)
ID#: Email: @ualberta.ca
Please, check your section/instructor!
Section Instructor X
EA1 V. Yaskin
EB1 E. Leonard
EC1 G. Tokarsky
ED1 V. Troitsky
EE1 V. Yaskin
EG1 S. Graves
Instructions
1. Place your U of A Student ID card on your table or desk.
2. The exam has 11 pages including this cover page. Please ensure that you have all
pages, and write your name at the top of each page.
3. The exam will be marked out of 60 points. There are 8 questions. The points for each
question are indicated beside the question number.
4. Answers for questions 1 through 7 must be accompanied by adequate justification.
Please note that this exam will be marked electronically. Anything written
on the back of the pages will not be marked.
5. For multiple-choice questions you are not required to show your work.
6. This is a closed book exam. No books, notes, calculators, cell phones or other
electronic aids are allowed!
,
3
1. [7 pts] Find the domain of f (x) = ln 2
− |x − 1| + |x − 2| − |x − 3| . Express the
solution using interval notation.
Solution.
Since the logarithmic function is only defined for positive values of the argument, we
conclude that
3
2
− |x − 1| + |x + 2| − |x − 3| > 0.
To solve this inequality, we consider several cases.
• Case x ≥ 3. In this case, |x − 1| = x − 1, |x − 2| = x − 2, and |x − 3| = x − 3,
hence the inequality becomes 23 − (x − 1) + (x + 2) − (x − 3) > 0. Solving this, we
get x < 27 . Thus, the answer for this case is [3, 72 ).
• Case 2 ≤ x < 3. In this case, |x−1| = x−1, |x−2| = x−2, and |x−3| = −(x−3),
hence the inequality becomes 32 − (x − 1) + (x + 2) + (x − 3) > 0. Solving this, we
get x > 25 . Thus, the answer for this case is ( 52 , 3).
• Case 1 ≤ x < 2. In this case, |x − 1| = x − 1, |x − 2| = −(x − 2), and
|x − 3| = −(x − 3), hence the inequality becomes 23 − (x − 1) − (x + 2) + (x − 3) > 0.
Solving this, we get x < 23 . Thus, the answer for this case is [1, 32 ).
• Case x < 1. In this case, |x − 1| = −(x − 1), |x − 2| = −(x − 2), and |x − 3| =
−(x − 3), hence the inequality becomes 32 + (x − 1) − (x + 2) + (x − 3) > 0. Solving
this, we get x > 21 . Thus, the answer for this case is ( 12 , 1).
Combining (taking the union of) the answers in the four cases, we obtain the final
answer:
( 21 , 32 ) ∪ ( 52 , 72 ).
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller xuyian222. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
73918 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now