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mth 174
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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text of prac. test #1
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question form
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Mth 174
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Question: Section 7.2 Problem 13
problem7.2.13 (previously 7.2.50 was 7.3.48) f(0)=6, f(1) = 5, f '(1) = 2; find int( x f '', x, 0, 1).
**** What is the value of the requested integral?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
I begin by letting u = x and u’=1
I let v’=f’(X) and v = f(x)
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The integrand is x f '', not x f '.
Unfortunately the font and the spacing of the document appear to obscure this. The first ' often looks like part of the letter f.
Having chosen u = x, you would therefore need to let v ' = f '' (x).
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So we let u = x and v ' = f '', leading to v = f ' and du = dx.
An antiderivative is therefore
u v - integral ( v du )
= x f ' - integral (f ' (x) dx )
= x f ' (x) - f(x).
The definite integral from 0 to 1 is thus
( 1 * f ' (1) - f(1) ) - (0 * f ' (0) - f(0))
= 1 * 2 - 5 - (0 - 6)
= 2 - 5 + 6
= 3.
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So now I use u*v-integral(u’v)
So I have xf’(x)-integral 1*f(x)
Xf(X)-integral f(x) the integral of f(x) is f(x) so we have
xf(x)-f(x)
we are told that f’(1)=2, F(1)=5 and f(0)=6
At this point I am confused on how to proceed, I
##??? I had the same steps as the given solution up until this point :
xf'(x)-integral of f'(x) ( I got this step)
Integral of f'(x) is f(x). So antiderivative is ( I got this step)
x f ' (x)-f(x) Why did the antiderivative become xf”(x) - f(x) instead of xf(x) - f(x)???
Besides this I am still having a hard time figuring the value of the interval. I think I should use the first fundamental theorem of calculus, and I know I evaluate at each value of the integral but I am confused. Could you walk me through this process and also if available provide me a formula like you did with the chain rule that would clarify for me???
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See my notes. You read f ' (x) where the problem had f '' (x).
This isn't entirely your fault, as the font and spacing of the original document made this difficult to distinguish.
I think that's your main point of confusion. Check my notes and let me know if you have additional questions on this.
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question form
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mth 174
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Practice test 1 emailed
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I emailed you a practice test #1 as an email attachment. I wondered if you could give me and idea of what my grade would have been if this were the real test,and also ask that you give me suggestions for improvement, and let me know which ones I got wrong or need to correct. I hope through taking a few practice tests I will feel more confident and be better prepared for the actual tests.
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I got the email. However I can't insert comments into a PDF.
On #4 you have the right general behaviors and did a great job translating the positive/negative behavior and positive/negative slopes into the increasing/decreasing behaviors and concavity of the integral.
However I don't think the graph of the integral ever goes negative, and if it does is doesn't go very far into negative values. The positive area accumulated between x = 0 and x = about 3 appears to exceed the negative area between about x = 3 and about x = 5.5, so there is never a point to which the accumulated negative area exceeds the positive area previously accumulated.
Past x = 5.5 the positive area overwhelms any negative area that follows. So even if there is a short interval over which the graph of the integral is negative, the value will never get close to being negative again.
I can't comment further on this because the problem is split between two pages and it's just too inefficient for me to flip back and forth. If you have additional questions on this problem and/or want to send a revision you're welcome to include a copy of your graphs on a single page so I can compare them directly.
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For #5 you have a good table of values for F ' (t), but to estimate F(t) you would forst need to graph F ' (t) and approximate the areas beneath the curve for the interval from t = 0 to t = .3, and from t = .3 to t = 1.6. It would be worth your effort to make these estimates.
Those areas correspond to the definite integrals of F'(t), so it's while it would be instructive and I recommend it, it's not actually necessary to estimate the areas associated with your graph. You can simply integrate F ' (t) from 0 to .3, then from .3 to 1.6, and use your results to find F(.3) and F(1.6).
Reminder on notation: You used f ' (t) for the derivative of F(t). The derivative of F(t) would be F ' (t), not f ' (t).
There is a convention in the text that f(t) can stand for the derivative of F(t), and with this convention you could label your derivative function f(t). But you would not want to label it f ' (t), which would be likely to cause you confusion.
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You did a very good job on #6, and would have received full credit, but your notation leaves me a little nervous. You will be more secure on problems of this type of you use a little clearer notation.
If dy/dt = t/3 + 1/3, then
y = integral(t/3 + 1/3 with respect to t) = t^3 / 6 + t / 3 + c.
You have this result but you called it dt.
Note that if y = t^3 / 6 + t / 3 + c, then
dy / dt = t / 3 + 1/3,
so it is indeed appropriate to say that for this situation, y = t^3 / 6 + t / 3 + c, or if we want to emphasize that y is a function of t, we can write
y (t) = t^3 / 6 + t / 3 + c.
Now, y(1.3) = 1.5 gives you the equation
1.5 = 1.3^2 / 6 + 1.3/3 + c
which matches your equation, and has solution c = .79.
Thus
y(t) = t^3 / 6 + t / 3 + .79.
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I think the last problem looks very good. I can't check it in full detail because it's split between pages and I can't keep track of details in the question while flipping back and forth. You're welcome to send a copy of the problem and solution on one page so I can check all the details. I think they're all there, but I really need to see the questions and your solutions at the same time to make sure you're answering the questions exactly as they are asked.
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I've included notes on the problems that required them. Problems on which I didn't include notes (and even some on which I did) would have received full credit.
You would have made a solid B on this test, and you're easily within reach of A work.
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Do sent me a text copy of the test questions themselves so I can file them for future use, along with my comments.
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Thank you for your notes and for your time in reviewing this practice test. I really appreciate your help and will continue to review for the first test. Below is a text copy of the test questions.
&&&Problem number 1
Find the indefinite integral of the function t^5 e^(t+3)
Problem Number 2
Find an antiderivative of the function f(t)=e^(8t)
Problem Number 3
Find the general antiderivative of e^(cos(8x)) sin (8x)/7
Problem Number 4
Sketch a graph of a continuous f(x) which is linear from (0 , 5) to (5, -2.001) then linear to (8 , 7) and then again linear to (13, -4.004). Sketch a graph of its derivative F(x) for which F(10) = 19 and label the known points on the graph.
Problem Number 5
If F’(t) = 3 sin(t) e^7y, then if F(0) = .5, find F(t) for t=.3 and for t=1.6
Problem Number 6
The depth of water in a container is changing at the rate of dy/dt = t/3+1/3. Find the depth vs. clock time function if it is known that the depth is y=1.5 when clock time t=1.3
Problem Number 7
Find the average value of y=9 sin(x) on the interval [.6, 1.7]
Problem Number 8
The rate at which water rises in a container is r(t) cm/sec, where t is clock time in seconds.
• Write an expression for the change in water depth between clock times t and t + ‘dt.
• Write a Reimann sum with n intervals expressing the change in water depth between t=9 and t=25
• If r(t) = .7t^2 +9t+98, then how much did the depth change between t=9 and t=25?
• If the depth was initially 2700, then what is an expression for y(t), the depth at clock time t?
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Great. Thanks.
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Here is a copy of the testing guidelines for MECC.
Please email me to acknowledge that you have read them, that you know where to find them, and that you will review them before arranging your test.
I'll also be sending a copy via email.
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MECC Testing Guidelines
The MECC Testing Center supports the college goal of providing quality student services that are responsive to the needs of current and prospective students. The Testing Center coordinates testing services for new and continuing students which include placement testing, ability-to-benefit testing, and testing for Internet courses. Upon adjunct faculty request, the Center will administer make-up test. In addition, students enrolled in distance education classes at other VCCS institutions may make arrangements for proctored testing.
· Testing Coordinator: Peggy Gibson at 276-523-2400, ext 283 or email pgibson@me.vccs.edu
The Testing Center, located in the Student Services Suite in Holton Hall, provides outstanding customer service by being courteous, responsible, and helpful. Tests are administered following appropriate testing protocol in a clean, comfortable, quiet, and secure testing environment.
The Center offers extended hours to serve students and prospective students, and the Testing Coordinator also arranges evening and Saturday testing with the Wampler Library located in MECC Robb Hall. (Request for special testing arrangements must be made at least 24 hours in advance.)
In order to ensure an accurate and fair process for all concerned, the procedures detailed below, must be followed:
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The Testing Center will maintain a proctoring log in which students will record the following information:
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· Each test to be proctored must be accompanied by an Instructor Transmittal Form completed by the course instructor. This form is available online or may be picked up from the Testing Center/Student Services
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· Each test and its Instructor Transmittal Form should be delivered to the testing center no later than two days prior to the date the instructor indicates the test is to begin.
· A beginning and ending date for each exam must be stated on the form.
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· Instructors must approve all items students may use when testing. The Testing Center will provide only scratch paper and pencil. Any other items must be authorized by the instructor and provided by either the instructor or student; this includes graph paper or calculators if needed. All scratch paper will be attached to the test upon completion. Instructors should make arrangements with the College’s disabilities coordinator (Dale Lee) if a student requires individual assistance or has special needs for testing. Testing Center policy, for security reasons, does not allow tests to be taken out of the testing center; therefore, the Testing Center cannot administer tests for a student with disabilities if that student requires individual assistance or has special needs for testing which prohibit the student from taking the test in the testing center.
· Instructors requesting changed deadlines, changes from requests on their Instructor Transmittal Form, or any other changed test information must submit such changes in writing (e-mail and hard copies). Please understand that telephone contact will not be sufficient for security reasons. Testing proctors are not authorized to provide tests to students after the testing period designated by the instructor has past. Only written approval for this from the instructor will allow this change of schedule.
· The Testing Center is not able to grade tests.
At the end of the testing deadline, tests will be returned to the instructor either in his/her College mailbox, or held for pickup by the instructor, as indicated on the Instructor Transmittal Form
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mth 174
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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mth 174 prac. test 1 ver. 2
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I have emailed a pdf version of the test with my answers to you. I took care to make sure each answer was on one page, I apologize that I didn't do that on the previous practice test. Pasted below is a text version of the questions from the test for you. I appreciate your help in reviewing these practice tests for me so that I can feel better prepared for the actual test. If there is another way you want me to submit the practice tests please let me know.
please also let me know how my grade would have been for this practice test as well as anything I need to correct or work on to improve my test.
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PRACTICE TEST #1 VERSION 2
Problem Number 1
Find an antiderivative of the function f(t) = 5*e^(7t)
Problem Number 2
The rate at which water rises in a container is r(t) cm/sec, where t is clock time in seconds.
• Write and expression for the change in water depth between clock times t and t+ ‘dt
• Write a Reimann sum with n intervals expressing the change in water depth between t=3 and t=26
• IF r(t) = .9t^2 + 3t + 62, then how much did depth change between t=3 and t = 26?
• If the depth was initially 3500, then what is an expression for y(t), the depth at clock time t?
Problem Number 3
Find the general antiderivative of 5 x^ 8 * e^(.7x)
Problem Number 4
Find the area between the graphs of y=9x/2 and y=sin(9x)
Problem Number 5
Find the indefinite integral of the function x(ln(x))^8
Problem Number 6
If water is rising at .37 cm/sec in a sphere of radius 30 cm then at what net rate in cm^3/sec is water entering the sphere when water depth is 29 cm?
Problem Number 7
Find the general solution of dy/dt = 8cos(9t) - .6
Problem Number 8
Find the integral of sin(t)/[9cos^7(t)], between t=1.9 and t=2.4 in two ways.
• First find an antiderivative of the function, in terms of the original variable t, and apply the First Fundamental Theorem.
• Then use an appropriate u= . . . substitution and rewrite the integral in terms of u. Don’t convert the antiderivative back to the original variable, but simply apply the First Fundamental Theorem to an antiderivative expressed in terms of u.
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Thanks.
No apology is necessary for the test you submitted. Everything was clear and legible and the only issue was a couple of 'split' problems, which you've corrected on the file you've sent.
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