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Unformatted text preview: Math 17B
Kouba Exam 1 (,IOV‘QQ'I’fc C] Your Name : ____________________________________________________ __ Your EXAM ID Number ________ __ 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. ‘ 2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY
WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS
A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM
ANOTHER STUDENT’S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR
CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE
KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE
EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK
YOU FOR YOUR COOPERATION. 3. No notes, books, or classmates may be used as resources for this exam. YOU MAY
USE A CALCULATOR ON THIS EXAM. 4. Read directions to each problem carefully. Show all work for full credit. In most
cases, a correct answer with no supporting work will receive LITTLE or NO credit. What you write down and how you write it are the most important means of your getting a good
score on this exam. Neatness and organization are also important. 5. Make sure that you have 7 pages, including the cover page.
6. You will be graded on proper use of integral and derivative notation.
7. You will be graded on proper use of limit notation. 8. You have until 10:50 am. to ﬁnish the exam. 1.) (7 pts. each) Use any method to integrate each of the following. DO NOT SIMPLIFY answers . a.) /cos 3$+sinx d9: . 4 (6 pts.) If y = f is an odd function and f f den = 5, then what is the value of
3 a . [:f(a:)dx? 3.) (8 pts.) The base of a three—dimensional solid lies in the region bounded by the graphs
of y = O, y = ln 3:, and at = e. Cross—sections of the solid at a: perpendicular to the :r—axis are rectangles of height 3. SET UP BUT DO NOT EVALUATE the deﬁnite integral which
represents the VOLUME of the solid. 4.) (8 pts.) SET UP BUT DO NOT EVALUATE the deﬁnite integral(s) which represents the AREA of the region bounded by the graphs of y : a), y :2 g, and y z 1. 5.) (8 pts.) Use the limit deﬁnition of the deﬁnite integral (for convenience, you may
3 choose equal subdivisions and right—hand endpoints) to evaluate / x2 dx .
1 6.) (7 pts.) The temperature T of a room at time t minutes is T(t) = V16 + t 0F . Find
the average temperature of the room from t z 0 to t : 20 minutes. 7.) (8 pts.) Find the length of the graph of y : (3/2)x2/3 on the interval [1,8]. 8.) (6 pts.) Let :zv/ eﬂdt. Find F’(1).
1 9.) (7 pts.) Use integration by parts twice with a twist to determine / sin 31!; cos a: do: . The following EXTRA CREDIT problem is OPTIONAL. It is worth 10 points. 1.) Use any method to integrate : / sin(ln 33) d1: ...
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This note was uploaded on 11/26/2010 for the course MAT Mat 017B taught by Professor Kouba during the Winter '09 term at UC Davis.
 Winter '09
 Kouba
 Calculus

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