12/08/2021
MATH 12002, CALCULUS I, TEST 4 NAME:
To the Student:
� Make sure that your camera and microphone work. Absence of a working camera could invalidate your
test.
� As soon as we begin, download the test 4 �le from Blackboard. Once in place, you should
1. Turn your camera on and point it to show the area on your desk that you are going to be writing
on.
2. Turn your microphone o¤. Activate it only when you need to communicate with the instructor.
3. Keep item (1) on for the duration of the test.
� If you have access to a printer and scanner, print a copy of the test. Present the problems neatly in
the space provided. You can use your own scrap paper. Once you are done, you have half an hour to
make a clean scan of your completed exam into a pdf �le and email it to me. Do not send me any
scrap paper you might have used.
� If you do not have access to a printer or scanner, use your own paper to neatly write your solutions
to the problems in order. Once you are done, you have half an hour to take well-lit and clear pictures
of your work, paste them to a Microsoft Word �le, in order, and email the �le to me. Do not send me
any scrap paper you might have used.
� In either case, name the �le by last name �rst name course number assignment number. For example,
Smith George MATH 12002 Test 4.pdf or Smith George MATH 12002 Test 4.docx
� All answers should simpli�ed and exact. Do not use decimal numbers. Answers with no work will
receive no credit. Each part of each question is worth 10 points adding to a total of 180 points for the
test.
� Good Luck!
1
1. Let f(x) = x2 + 1, P = f�2;1;2;5g. Find the left and right Riemann Sums for f over the partition
P. What is kPk ?
2. Find
Z 1
0
(x2 +x)dx by taking the limit of Right Riemann Sums, over a uniform partition of [0;1].
3. Find lim
n!1
�
2n
nX
k=1
cos
k�
2n
2
4. By interpeting the integral in terms of area �nd
Z p2
�
p
2
p
2�x2dx
5. For the following, compute dy
dx
:
(a) y =
Z x
0
1
t3 +1
dt
(b) y =
Z x2+1
0
p
costdt
(c) y =
Z xex
1
sin�
�
d�
(d) y =
Z y sinx
0
et
2
dt
3
6. Compute the given integral.
(a)
Z 2
1
(3t2 �4t+7)dt
(b)
Z
tan4 xsec2 xdx
(c)
Z e
1
(x�
1
x
)dx
4
(d)
Z
x
p
x2 +1dx
(e)
Z
x
p
x�1dx
(f)
Z e2
e
lnx
x
dx
(g)
Z
x2
3
p
x3 +8
dx
5
7. Find the area of the region bounded by the graphs of f(x) = 8�x2 and g(x) = x2.
8. Compute the value of limx!0+
R p
x
0
t4 sintdt
x3
9. Suppose that f is continuous and
R 2
0
f (x)dx = 3. Compute
R 2
0
�
1+
R x
0
f (t)dt
�2
f (x)dx.
6
Why Choose Us
- 100% non-plagiarized Papers
- 24/7 /365 Service Available
- Affordable Prices
- Any Paper, Urgency, and Subject
- Will complete your papers in 6 hours
- On-time Delivery
- Money-back and Privacy guarantees
- Unlimited Amendments upon request
- Satisfaction guarantee
How it Works
- Click on the “Place Order” tab at the top menu or “Order Now” icon at the bottom and a new page will appear with an order form to be filled.
- Fill in your paper’s requirements in the "PAPER DETAILS" section.
- Fill in your paper’s academic level, deadline, and the required number of pages from the drop-down menus.
- Click “CREATE ACCOUNT & SIGN IN” to enter your registration details and get an account with us for record-keeping and then, click on “PROCEED TO CHECKOUT” at the bottom of the page.
- From there, the payment sections will show, follow the guided payment process and your order will be available for our writing team to work on it.