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Unformatted text preview: Math 16A (Fall 2005)
Kouba
Exam 3 KEY  Please PRINT your name here : _ __T__ ____ _ .. __ Your Exam ID Number ............ _ I. PLEASEVDO 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. PLEASE
KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE
EXAM SO THAT OTHERS WILL NOT BE TEMI’TED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION. 3. COPYING ANSWERS FROM A CLASSMAT 3’s EXAM IS A VIOLATION OF
THE UNIVERSITY HONOR CODE. ‘1. No notes, books, or handouts may be used as r<~2sourccs for this exam. YOU MAY
USE A CALCULATOR ON THIS EXAIVI. 5. Read (lirections to each problem carefully. Show all work [or full credit. In most
cases. a correct answer with no supporting work will receive Ll'l"l‘l.,.lil 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. Neatmass and organization are also important. 6. Make sure that you have (3 pages, including the cover page.
7. You will be graded on proper use of derivative notation.
8. Include unitson answers where units are appropriate. 9. You have until 10:50 am. sharp to ﬁnish the exam. 1.) (5 pts. each) Differentiate each of the following functions. DO NOT SIMPLIFY
ANSWERS. a.) 31:21:29.7: {— :05 :2, y’: ﬁve/(sij‘Zs? + 2X (3mg)? 1).) fa) :3 Iva: wq v l v wij
i, web—3g; . a ﬂgixjéfajt c.) y : sin3(gX) L )1; 3 MQ(3\X)~ M (ax)' 3x 2.) (5 pts. each) A ball is thrown straight up at 64 ft./sect from the top of a build— ing which is 80 ft. high. It’s height IL above the ground after t seconds is given by
hm z ~~16t2 + 64$ + 80. :L) [low high does the hull go ? 14(66): 326 {,tLl: o ——5 ﬂ: 9? M.
WA WV: ~/e («omega/7L 9’0 1'. 14"} ﬂ». b.) How long is the ball in the air 1’ M 1 hat—2:0» o:lé.ézi—é<—l+ 4—90“, 4666’; q+~57= ’16 E“ 57C‘H// "’ @J' c.) What is the hall‘s velocity as it strikes the ground ? “((5): "32(5771164 : ~1Go+6<1 : “"0 4>h/4o.g. 3.) (10 pts.) The volume of a cube is morensmg at the rate of J m./sec. How fast is the
surface area of the cube changing when each edge is 2 inches; long? 4.) (10 pts.) Assume that y is a function of and 3/3 + xy :2 8 . Find an equation of the
line. perpendicular to the graph of this equation at :5 : 0. yaw: 8 93—» 3j2y1¢><>ﬂ+0‘yto '4 (372440)” a “7"? 7,: i2 ‘ 5.) (10 pts.) Determine all inﬂectim points (2:, y) fer the graph of ﬁx) 2 sting: + 603:1: on
the interval [0, 2w]. DO NOT GRAPH THE FUNCTION. \ H ‘
4909: Cody—.an «LCM: “’wa covx :o *9 ,1; r
~MK:%X"”‘ MK :"(twiéz 44‘
«5/ we» 3T 02 2 / ~// J __ /
m —» — :37r ~77 :5
1:”. 7:0 jzo 9 2* 6.) (20 pts.) For the following function f state the domain and determine all absolute
and relative maximum and minimum values, inflection points, and x and y—intercepts.
State clearly the xw'alues for which f in increasing (T), decreasing (t), concave up (U), and concave down (ﬂ). Find equations for all vertical and horizontal aSymptotes. Neatly
sketch the graph of f. f(x'):_._£_ 1 all mm $2 + l 412x): W ~ lel '0 94+le ” 0649*” 7.) (10 pts.) Determine the x—vahles for which the following function is increasing and
decreasing (i). DO NOT GRAPH THE FUNCTION. 2 $2 — 32\/;1}~ 8.) (10 pts.) The radius 1‘ of a right, circular~ COWE, is increasing at; 3 cm./sec. and
the height h is decreasing at «1 (tin/sec. At, what; rate is the volume of the cone changing
when r r: 5 cm. and II. :2 6 cm. '? Assunm that, the volume 0sz COH‘L 'is V (1/3)nr2h. 0\ V‘ W 
M ; 3 . 4%. ~ 4 w. v EXTRA CREDIT PROBLEM~ The following problem is worth 10 points. This problem
is OPTIONAL. l.) A watermelon is dropped from a height of 224 feet.
from where you are standing. How fast is the
changing after it has fallen for 3 seconds ? (AW: ——/{%2+2¢’(‘/
Q We):wa
,LféZS’xyvcv/ “(3/3 90/ W
g:(oo ‘ W l l i J l O\ $041+ Glee/sz 82 w?? It will strike the ground 60 feet
distance between you and the watermelon i \ .
l \\\. £12 : “‘9
WA \f a: 0W l f
i \ [60 X0 _76 ...
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This note was uploaded on 11/14/2010 for the course MAT MAT 16 A taught by Professor Kouba during the Spring '10 term at UC Davis.
 Spring '10
 Kouba
 Calculus

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