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Unformatted text preview: Math 16B (Spring 2010) Kouba Exam 2 Please PRINT your name here : _____i_<___é___j: ________________________________
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 TAKE AN EXAM FOR
ANOTHER PERSON. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH
AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED
OR DIST RACTED. 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 6 pages, including the cover page.
6. Include units on answers where units are appropriate.
7. You will be graded on proper use of integral and derivative notation. 8. You have until 10:50 am. sharp to ﬁnish the exam. PLEASE STOP WRITING IMMEDIATELY AND CLOSE YOUR EXAM WHEN TIME IS CALLED. THANK YOU
FOR YOUR COOPERATION. 9. You may use the following trig identities : a.) sin2 6 + 0032 6 = 1
b.) 1+ tan2 6 2: sec2 6
c.) sin26 = 2sin6cos6
(1) cos 26 = cos2 6 — sin2 6
= 20082 6 — 1
= 1— 28i1126 1.) (7 pts. each) Determine the following indeﬁnite integrals. a.)/(ex+1)(ex—2)dm :_ S<€&X_ ex Q)M  36°22: ex&x+c, m/(lnfgdx (i371— uzﬁnxQ» Mziér]
—~ SM3AM : Luq+c LCMX)L/+C/ _ q , q (x+2)2 XZU"<1/
: 3 “‘Cu‘a) M
M;
n —;z I
2 S 3)“$4M I 3C3 (A ~ a—‘JJA’L
_. ~I
: 3 g,’~;zmu[+¢ : ~ 3 Lx+aj~}m{x+;l +0, 3
:: ~Mx+~§@o<1><) +Q/ 3 1:3 ‘2.) (7 pts.) Compute T4, the Trapezoidal Estimate using 71: 4, for / m + 2 d9: . 3
3 1 1 x .
‘+—’—‘l—~#~—+——+ h: 4f 2 :1) {lg}: x+A )
: 77,3. [th I)+— Q‘PCO}+ 02 4102+ 246512+ 4(3)]
.. ,. l —_l___5—+ _(___O
_ §[*l+e160)+&(3)+2éj+°?§ __ .— 5+ 54—649 5.  136» ~ é?
‘1'73:~ ,5 “4/5/33 3.) (7 pts. ) Rain 15 falling 1n Davis at the rate of (1/10) inches per hour at time t hours.
Determine the total amount of rainfall for 1 < t < 4. 4i 2M
_ L+
TOTAL — 3, [7‘0 7, _L . i
03 .—
_ .é, 4.) Consider the region bounded by the graphs of y = (/5, :c = 4, and y = O. a.) (6 pts. each) Compute the AREA of the region using j
i.) vertical cross—sections. AREA : Sjﬁ‘M 11.) horizontal cross—sections. AIQEA: Sits—ﬂ} 4y
2. /
:m— gmto : e— 900) :1qu ‘—
‘_——' 3,3 5
.— L‘:
3 b.) (6 pts.) Find the VOLUME of the solid formed by revolving the region about the
LIEaxis (SET UP BUT DO NOT EVALUATE THE INTEGRAL(S).). vM :. 7834M : 1T Q’s/mad %; c.) (6 pts.) Find the VOLUME of the solid formed by revolving the region about the
yaxis (SET UP BUT DO NOT EVALUATE THE INTEGRAL(S).). Vol/W : TT SZ‘IQRGly ~ Trgi‘wldy
7. ’H‘SjG{fady _ ”IT‘S: (D’RJD‘OQ), d.) (6 pts.) Find the VOLUME of the solid formed by revolving the region about the line y = 3 (SET UP BUT DO NOT EVALUATE THE INTEGRAL(S).).
g? (3 VM : Ti" EZRZOL’X — TFS:Y‘9‘0K¢(
Ll
: TFSO (gjxw ~_ Tj:<3—\/33)20L¢( 5.) (7 pts.) The height of a palm tree is given by H : (1/2)tv t2 + 9 feet at time t years.
Find the AVERAGE height of the tree for 0 S t g 4. I EXTR CREDIT PROBLEM— The following problem is worth 10 points. This problem
WT ONAL. 1.) / A
u‘ sin 2: —968T——sina: (1.1:
w“ .
MX ~ MX MX+MK
meLMX M ...
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 Spring '10
 Kouba
 Calculus

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