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Unformatted text preview: Math 21B (Winter 2006)
Kouba
Exam 1 Please PRINT your name here : _________________________________________________________ __
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 VIO
LATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM SOME—
ONE ELSE’S EXAM. 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 NOT receive full 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 11:50 am. to ﬁnish the exam. 1.) (8 pts. each) Integrate each of the following. DO NOT SIMPLIFY answers. a.) +;I:) (1:1,, d.) ——(3x2+1)4 (11: e.) /sin2x coszz: d3: 2.) Consider the function : are“. a.) (6 pts.) Verify that f is an odd function. 3
4 b.) (4 pts.) Evaluate/ 1361' (151;.
—3 2 2 —1
3.) (6 pts.) If/ f(a:) d1} = 3 and / j'(m) (11' = ~4 , what is f(:c) d3: '?
~1 0 0 4.) (12 pts.) Use the limit. definition of the definite integral (for convenience, you may
.3 Choose equal subdivisions and righthand endpoints) to evaluate / (1122 + 21:) (1:1: .
. 0 5.) (8 pts.) Compute the area of the region bounded by the graphs of y = :32, y : 2 — :L‘, and y = 0.
a!” 6.) (8 pts.) The temperature T of a room at time t minutes is T(t) = \/16 + t 0F . Find
p the average temperature of the room from t = 0 to t = 20 minutes. 7.) (5 pts. each) Use FTCl to differentiate each function. 4
a.) F(m)=/ cos tdt 8.) (6 pts.) Write the following limit as a deﬁnite integral, then evaluate the integral.
HINT 2 First identify mi. “1320 219%}3 The following EXTRA CREDIT problem is OPTIONAL. It is worth 10 points. 1.) Use the limit deﬁnition of the deﬁnite integral, lim 2 f(ci)(:ni — m4) , to eva1u~
mesh—)0 ’L:
b
1 . . . .
ate / —— da: . Use an arbitrary partmou a : 110 < :171 < 1'2 < < :17”__1 < :17” = b for the .2
. a (L I . .
interval [(1.1)] and samphng numbers (31‘ = for z =2 1. 2‘ 3. .n. ...
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This note was uploaded on 04/16/2008 for the course MATH 21B taught by Professor Vershynin during the Spring '08 term at UC Davis.
 Spring '08
 Vershynin
 Math

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