Review the file and answer all the questions

Hello, I would like from you to review the file and answer all the questions The answers should be detailed as much as possible. Also, Do not forget to do the last question in the last paper which is called The critical thinking question. It is the most important question in the file.Thank you
_20_activity_14_final_exam_review.pdf

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MAC 2311 Final Exam Review
Pre-Assignment. These questions contain a small selection of review problems from your
review sheet for your final exam. Print out the activity and do the first problem.
Print out the activity and do Problem 1. Bring your activity and pre-assignment to class.
Once you have completed this pre-assignment, go to the Canvas page for your class and
complete the pre-assignment quiz that you will find there. You have as many tries as you
like for each question. This must be completed BEFORE your peer led session on Friday.
Bring your printed activity with your completed pre-assignment to your peer led session in
order to be eligible to take the quiz that will occur at the beginning of your peer led session.
(That quiz will be based on your most recent activity.) If you need help completing the
pre-assignment, feel free to drop in at SMART lab (at the library tutoring services).
SMART lab Hours are:
M Th: 9am–9pm
F: 9am–4pm
Sa: closed
Su: 1–5pm
1. Simplify (so that your answer contains no trigonometric or inverse trigonometric function):

-1
cos tan

2
=
x
2. If f (x) = x2 – 2x for 0 = x = 3, evaluate the Riemann sum with 6 subintervals, taking
right endpoints. What does the Riemann sum represent? Illustrate with a diagram.
3. Max and Minnie are going camping, and want to buy a water bottle that can hold 1000
cubic centimeters of water but has the smallest surface area, so that it will absorb heat
more slowly. Assume that the water bottle is a perfect cylinder with a top and a
bottom. What are the dimensions (height and radius) of the water bottle that they
are looking for?
4. A particle is moving with acceleration given by a(t) = 10 sin t + 3 cos t, in feet per
second per second, and t is time in seconds. If s(t) is the position of the particle at
time t, find a formula for s(t), given that s(0) = 0 and s(2p) = 12.
5. Compute the integral
Z
1
4
v
y-y
dy =
y2
6. Sketch the graph of the function f (x) = x4 – 8×2 + 8 by finding: domain, x and
y intercepts, intervals of increase and decrease, local extrema, intervals of concavity,
inflection points. Label your graph with all these items.
7. Evaluate the following definite integral by interpreting it in terms of area. Sketch a
picture that supports your answer.
Z
0
1+
-3
v
9 – x2 dx =
Activity Report – Review for Final Exam
We verify that we all understand and agree with the solutions to these questions.
Group Number:
Manager:
Recorder:
Spokesperson:
Strategy Analyst:
Critical Thinking Question: to be agreed upon by the group, and written below by the
R 1/x
recorder. If F (x) = 2 arctan(t) dt, what is F 0 (x)? Be sure to STATE which theorem you
are using, and explain your answer using a sentence or two. Don’t forget to write your names
and UIDs.
For instructor’s use only
All questions on activity filled out
Names and U-Numbers PRINTED on activity report
Critical thinking correct, fully justified, and written in complete sentences
Satisfactory/Unsatisfactory

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