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Unformatted text preview: Name: MA 1021  2008 A Term Section 2 —. .. .. . _
Saptember 25, 2008 Quiz — Sections 3.6, 3.17, 3.3 1. What is Dx[sinx]?
(2p0ints) 2. What is Dx[cosx]?
(2190mm) 3. What is Dx[secx]?
( 2 points) _. 4. What iS Dx [tan x] '2
( 2 points) 0 5 What is 608(3/6)?
(2 points) Part 1 6. What is tan(7r/3)?
(2p0ims) 7. What is cos(57r/ 6)?
(2points) 8. What is Sin(—7r/ 2)?
( 2 points) . Could John Paul’s Calculus
name be either John or Paul
today? If so, which one? If not, what is it and why?
(BONUS 2 points) 10.What color is the bear?
(BONUS 2 points) *************** END OF PART 1 **************** Name:
MA 1021  2008 A Term Section 2
September 25, 2008 Quiz — Sections 3.6, 3.7, 3. 8 Part 2 For the following problem, set up the optimization problem, but do not solve it. Your ﬁnal answer should be' in the form: Find the minimum/maximum value 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. And make sure: you follow the format shown above to formulate your answer. 1. The product of two numbers is 5000. Each of the numbers is greater than
or equal to 5. What is the largest possible sum of the two numbers? (10 points)
Le} x anal 3 rafﬂes“! “the +1115 mum
S = X+ 5
Pu; X115500C>é 3:30”
X 500:)
x Maximize SOC) sulajec! to He awe» alum?“ S(X): X+ 53x5... berg. woo" For the following problem, set up the optimization problem, but do not solve
it. Your ﬁnal answer should be in the form: : Find the minimum/maximum value of f (x) = [function],
subject to A S x g 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. And make sure; you follow the format shown above to formulate your answer. 2. You are a bookseller, about to the publish a new autobiography, “The Life of John Paul — Pope or Calculus Student?” Market research indicates that if you give the books away, 100,000 people will want one; but for every :
dollar you raise the price after that, demand will fall by 1,000 people (so ,_
for example, if you charge $3 for the book, only 97,000 people will buy it). .
In order to publish the book, you must buy a $30,000 printing press, and :
spend another $50,000 for John Paul’s lavish worldwide publicity tour,
promoting the book. 'In addition, it will cost $2 per book to actually print i
the books, for labor and materials. How. much 'should you charge for the book in order to maximize your
proﬁt? Let’s call x the price of the book. (12 points) ' From .5 Revenue— cosi
Revenue —:.'(pn'ce)(laool<s Sold)
Frt’ce :.. x I i
book: Soul '5 lagoon—— Loocx I
605+ =‘ 30,06os S'o,ooo + 2t(loo,ow quack) Cost = 230,060 2,000x
Reva ﬂuez. (x) ( Iooooo  [coax , Pmﬁ¥¢P(X)I.=
05.x :5 too
M‘lene 5u5JQ¢+ +3 "EL 5tv¢~d¢1mt X)(loo,ooo —I,ooox)— [236,x . You are hiking in the Grand Canyon. You look across at the other side,
when suddenly to your surprise, a cow has just fallen into the canyon,
exactly even with your eye level. With your bionic eye, you are able to track the angle of depression 9, how far below horizontal the cow appears (see picture). The canyon is 3000 feet across. When the angle of
depression reaches 35 degrees, it is increasing at a rate of 2 degrees per second. Set up but do not evaluate an expression for the downward speed of the poor cow at this point. (12 points) For the following questions, you are given: Dx [sin x] = cos x Dx [cos x] = — sin x Dx [tan x] 2 sec2 x Dx[sec x] 2 sec x tan x Dx[®] = e 4. Find the derivative of each of the following functions (6 points each unless
otherwise indicated) a if(x)=x3sin5(x) I?!) = (3x1) {sin Sx) ! (x 3)(§S;nyx Caggc.) b. g(x)=ex+xe+\/P7r_e
 x eI_
gyne e + ex sin x — tan2 x d y— 5 _ ; (x2+3) Z: i 5”" (Cosxv 2+1” Sec‘x)(x‘+5‘)S—— 5(X1+Z)V(Zx)(5rﬁx_{13x) _.
. (X21L3)IO I 3602 x e. y = x (use logarithmic differentiation) [n3 —; in x5“ ” '; (Secex) A x _ ,2 i
.. _, lsecx (Secx'fanx)ﬁwx 4 sec x 7; i:
'1 Ax x I 9:? 1 (Xseczx) surf/sec): (an): fax 4. 255235 D a": 3(’Q~(+am)]z J“ §ec’?X
+mx
(1+ x2 )3/2
g. y : "mm—W (use logarithmic differentiation)
(1 + x ) .lnbg [h(l+K1)"%ant~x3) \M 9 2" _ ‘i’. ‘25:.
5 Ex: :2 l+x" 3 In)?
3/
duh (mifﬂ jg;_ w
at»: ’ (Huff/3 "*"1 1+x’
b. y = 669 (3p0ints)
® ®
4:1: 6 4...? , e $ olx dxi ...
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 Spring '08
 TASHJIAN
 Calculus, Optimization, John Paul, speciﬁc optimization problem

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