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Unformatted text preview: Name:
MA 1021 — 2009 A Term Section A02
September 28, 2009 Quiz  Sections 3.6, 3.7, 3. 3 Part 1 . What is our TA’s ﬁrst name
(spelling countsl)? . The (base ‘10) of
1000 is 3. Fill in the blank — and
no abbreviations, plus spelling
counts again! *************** END OF PARTl **************** Name:
MA 1021  2009 A Term Section A02
September 28, 2009 Quiz — Sections 3.6, 3.7, 3.8 This quiz contains two parts, with an assigned point value as shown below. No
calculators, notes, or books may be used on this quiz. No additional time will be
given beyond the end of class to ﬁnish the quiz. You may earn partial credit on
some questions, so be sure to show your work and/or explain things that you want
me to be aware of! Problem Points Score Part 1 I
p—nr—u
CDU‘I Part 2 U} HI
i—tr—diu—Ir—t
OOCDCD i— a—I i—t
Ui CD CD For @ quiz, you are given the following extremely useful information. Note
that this information may not be available on future quizzes, and it will likely
NOT be available on the Final Exam (which will be held on Wednesday,
October 14, at 7:00 pm, by the way). Dx Slnx]=cosx Dx[lnx] :1
x Dx 008x]: —sinx
Dx [ex] = 9" secx] =secxtanx lnA+lnB=ln(AB) Sin2x+coszx21 ‘lnA—lnB=ln(A/B) tan2x+1=sec2x ln(ek)=k 0 There are more than 10 million bricks in the Empire State Building. 0 The average lead pencil will draw a line 35 miles long or write
approximately 50,000 English words 6 Beetles taste like apples, wasps like pine nuts, and worms like fried bacon. This is what “Set up the optimization problem, but do not solve it? means:
Your ﬁnal answer should be in the form: ' ‘F ind the minimum/maxiMum vqlue of f (x) = [function], subject to A S x S B Remember, you don’t need to come up with a numeric solution — just write
down the speciﬁc Optimization problem that needs to be solved. A J 1. Set u the o timization roblem but do not solve it: A Norman window with perimeter 200 consists of a semicircle atop a rectangle, as shown in the
attached sketch. Find the largest such window as a function of x, the height
of the rectangular portion of the window (as labeled in the picture). 2. Set up the optimization problem, but do not solve it: Three sheets of
paper, each 4” by 6”, have four small squares cut from their corners. All twelve resulting small squares are the same size. The three large cross—
shaped pieces are foided into open top rectangular boxes, and the twelve
small squares are taped together to make two small cubes. Find the
maximum combined volume of the ﬁve boxes created by this process. '7; (vices: _  _ V: x Mb): mne HM ‘Rnc'hoin Wm: 3(‘i~2x)(é—Zx)(x)+ 2%;
subjeri +0 3. Find the area of the largest rectangle with its base on the Xaxis, to the right
of the yaxis, to the left of x=12, and beneath the parabola y = x2. E evaluate. A’Gq: qu—Bx" :— Bx {8—x) A7131; 0 hulkEn X7: (3 UM X113
A?!) emsh 'FW 4” X x ACK)
0 0
8 25¢, é“ [0132:4 fed—ILan 17.. O 4. You are watching a rocket launch from a point some distance away from the
spot directly below the rocket. When the rocket is 400 feet away from you (on a direct line of sight), its angle of elevation 9 from your perspective is
60 degrees, and is increasing at 1 degree per second. How fast is the rocket
rising at this moment? You can leave your answer in an unreduced form. 5. Eind gxz if y = sin(5x)cos(7x) “[15 5; 5605' (Ex) Cos ('17:) + 5&6") [‘7 5"“ (7x31
01x —Wm%mwmmmwm.wmu_wummwm. HMM.M¥.#_~_“_.W¥__##APA‘ dy 6. Find—ify=x dx tan x dy
7. Find — if =
dx y sec(x3 ) 63x 2 3 dy (x—l)(x2 — 2) (x3 — 3) 8. Findaif y: (x4_4)4(x5b5)5 9mg: mm) + awn) made2» 4% (9‘4) ~‘§ﬁ~!x’r) 2 1 zrx"
m .. .._+ L 22.4.,“  ~——,
‘\ 0\K' x~l 33—2 x1“? X‘LH “5'5’ *************** ************** ...
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This note was uploaded on 10/13/2009 for the course MA 1021 taught by Professor Tashjian during the Spring '08 term at WPI.
 Spring '08
 TASHJIAN
 Calculus

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