Due 11:59pm, Wed September 1st , 2021
Math 251 Unit 5 Quiz - S21
First Name
Last Name
OSU Student ID #
This quiz has 5 pages, 7 questions, and a total of 50 points.
Instructions:
• Access the Unit 5 Quiz assignment in the gradescope course for the Unit Quizzes. By downloading
the “template” your quiz timer starts and you have 120 minutes to complete, scan, and
upload your quiz.
• Do all of your work on this paper. Scan the completed problems and create one PDF of your
work. Your PDF needs to be at least the same number of pages as the original document.
• IMPORTANT: On this quiz and future quizzes, your exam may not be graded if
it is not submitted properly. To ensure proper grading and to minimize the need
for regrade requests, please make sure you exam has the correct number of pages,
in the correct order, and that answers are in the correct place on each page.
• Upload the PDF to this assignment in GRADESCOPE by the due date.
(The Gradescope assignment can be accessed through Canvas.)
• If you cannot or don’t want to print out this exam: Please use your own blank paper and
put your answers in roughly the same place on each page as they would go on the printed out
exam.
• Tablet Use: If you are using a tablet to write digitally on the PDF that is acceptable.
Allowed Items: (Please do not use any other items that are not on this list.)
• Pencil & Eraser (other writing implements are acceptable)
• You many use the following online scientific calculator: https://www.desmos.com/scientific
Note: this is NOT a graphing calculator. Graphing calculators are nor allowed on
this quiz.
• You may ask your instructor a clarifying question via email or in office hours.
• You may use any of the class materials available in Canvas.
1. (0 points) Before uploading my exam, I have verified my submission is 5 pages long and I have my
solutions on the same pages, with the same spacing as the template. I understand that my quiz
will NOT be graded if the pages are in the wrong order or orientation. See the bullet point labeled
IMPORTANT above for more information.
Yes
2. (6 points) Given the differentiable functions f (x) and g(x), and their derivatives in the table below,
find the value of the following limit. Give the solution along with your supporting work.
x
f (x)
f 0 (x)
g(x)
g 0 (x)
0
1
1
0
5
x + 3g(x)
=
x→0 1 − f (x)
lim
3. (6 points) Determine the value of k so the function, f , is continuous at x = 4. Give the solution
along with your supporting work.
 √
 kx 0 ≤ x < 4
f (x) =
 x+6 4≤x≤7
k=
Page 2
4. (4 points) In a kind of savings account, the amount of money is given after one year by the function
S(t) = S0 e10r , where S0 is the initial deposit, and r is the interest rate.
If the interest rate is 4%, the amount of money after one year is $7,420. When the interest rate is
5.3% the amount of money after one year is $8,920.
What property of this function guarantees that there is an interest rate between 4% and 5.3% that
gives $8,000 in the account?
5. (4 points) Evaluate the following limit.
90
lim √
x→∞
x
90
lim √ =
x→∞
x
Page 3
6. (10 points) Fill in the circle next to your selection for each question.Note that you are not being
asked to calculate these limits.
(a) Can l’Hopital’s rule be used when evaluating the following limit?
cos(7x)
√
x→0 4x −
x
lim
Yes
No
(b) Can l’Hopital’s rule be used when evaluating the following limit?
x2 − 4
x→2 x2 − 9
lim
Yes
No
(c) Can l’Hopital’s rule be used when evaluating the following limit?
ln(x + 1)
x→0 ex − 1
lim
Yes
No
(d) Can l’Hopital’s rule be used when evaluating the following limit?
e3x − x2
x→∞ e4x (x2 + 6x)
lim
Yes
No
Page 4
7. (20 points) Sketch a graph of a function, f (x), that has the following properties:
• f 0 (0) > 0
• lim f (x) = −∞
x→−∞
•
• lim− f (x) = ∞ and lim+ f (x) = ∞
lim f (x) = 3 and lim + f (x) = 1
x→−4−
x→3
x→−4
x→3
• f 00 (x) < 0 on the interval (−∞, −4)
• f > 0 on the interval (3, ∞)
• f 0 (x) < 0 on the interval (−4, −2)
• f 0 < 0 on the interval (3, ∞)
• f 0 (−2) = 0
• lim f (x) = 2
00
x→∞
Page 5