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Unformatted text preview: MATH 124 EXAM III FALL2009 MTH 124 Exam 3 Fall, 2009
KEV
Name: " / Section #:
PH): Date:
Instructions:  1. DO NOT OPEN THIS EXAM UNTIL YOU ARE INSTRUCTED TO DO SO. 2. Without fully opening the exam, check that you have pages 1 through 7 and that none
is blank. 3. Fill the information at the top of the page. 4. Neither books nor scratch paper are needed for this exam. Clear your desk of
everything but this booklet, your pencils and your calculator. If you need more space
to write your solutions, use the backs of the exam pages. 5. Crib sheets (pro—compiled lists of formulas or other information) either written or in a
calculator are speciﬁcally forbidden. Use of a crib sheet of any kind on this exam
will result in an automatic zero grade. 6. The problems on this exam vary in difﬁculty. You should try to solve these problems
in an order that will maximize your score. Solve all the easier problems ﬁrst, then go
back to the ones that require more thought. ’7. Unless otherwise indicated, SHOW ALL YOUR WORK. if no work is shown, no
partial credit can be awarded. Even for calculator solutions, you should include
relevant information, like the equation to be solved, the function whose graph is to be sketched etc. Your work and answer need to be accurate and relevant to receive
points. 8. Please place your answers in. the boxes provided. You may give only one answer. 9. Give simpliﬁed and exact answer; Unless you are speciﬁcally instructed to do
otherwise, DO NOT ROUND YGUR ANSWER. 10. You will be given exactly 50 minutes for this exam. I have read and fully understood all of the above instructions Signature: Page 
MaxPoints 10 l 28 t 22 is ‘ 15 g 10 100
i
3 Points  J a g b air‘sihrmles eschew (1425M ’ MATH 124 EXAM HI . . 3:00 in __ FALLZOOQ. 1. (10pts.) The graph of the derivative g‘(x') (not g(X) ) is Shown in the sketch above. _
Use this sketch. to ﬁll in the missing vaiues in the table for g(x) (not g‘(x)) given that g(2) = 4. S 0w some work to indicate where the numbers are coming from. E j . 5 «4‘. "V a...” :'; mum,ng gqu (Q E Sofa a MATH 124' EXAM III . 3:00 In FALLZOOQ 2. (5+5‘+5215pts.) Short answer questions. .. a x222 r t,ten ’x: 3. [)IfG()%1l1n()d h G() x th‘xl
[Club Lilla “Ml; “:2 O b) Suppose Jﬂﬂdic = 5 , and Ig(x)dx = 8 . Then we get that \9
“’ a by b b i ,
[yon )dx: g stay.) (in 45 3:? gm 2 s S lem t q L900 is:
a a. On a ‘
“lg 3: aUSHegftiél Momma gm
4 c) If f(x)dx = 7, and ]f(x)dx = 4, then [foam m {" Ltﬂzlxt ‘ltcmmgn‘lmclm => LN. gait—(>0de S. S t q Lt form = ethnic—tie
3. (9+4=13pts.) q 21) Write the area enclosed by y = x and y “xx2J3 as a single deﬁnite integral. Please specify the exact limits of the integration. (Hint: First ﬁnd the points of intersection of the
two curves.) ytk/ A
38:14 ‘7» xx}.— LlM’QD
XLWLlVO
x2109 “XiLl b) Evaiate th integral from part (a) by using your calculator. ﬂ QQCOQ}? MATH 1'24 EXAM HI 3.100 m . . FALLEOOQ 4. (12pts.) Find the equation of the line tangent to'the curve g(x) '= «#15 4 3x atx =E‘ 5. {6+4m10pts.) Suppose C(q) is the total cost (in doﬂars)required to setup an industry
and produce q units of a product. The ﬁxed costs in C (q) are $25, 000, and the marginal cost is C’(q) =‘0.008 92 +641] +38. In its ﬁrst month of operation, the industry
produced 200 units. 8.) Find the total cost to produce the ﬁrst 200 units.
(Cm) ‘3 C (.0) IF SW6 (3) 0%
b {50 it: “aéwooa «Ii (“wig imgﬂﬁd‘g “SB£3; 000 Jr mocca 'W b) Explain the practical meaning of the integrai and ﬁnd the result (including the
220 units) of jc'(q)dq ' 200 Exp»; cm 3:0 mWWQ (9%de Wm 3m “i5?” “m? W 0925)de 3% a \img _ r3239 MATT1.124 EXAM 111 3100 m . . .. PAM.2009 QWW “3m
6. (5+5+5$1.5pts.) Find the derivatives of each of the following functions. Do 113% simplify. .
Jan's; lﬁqtaw +0 i 3‘ 95¢“
a)y=6x3+52x*1+100 ysﬁgﬂ’sx) Jr‘s (L WA 2 \g y; Jr 5 SW3 L3
«3* . . , , ,1
13) MA) = (x +111x)4 E a 3 ~.: Lt manx9 L t” +31)“ 334 r, Ln! 1......4 WWW“)
c) g(x) = 236W __ 1 . m 635.5%] z’afwd “"5 (QR) %.%X““§’ CLAW“ m “3* L6 X”7)<JX 4:"«%\Xﬁ%~
L‘J Scratch Work: .. _ ( MATH 124 EXAM III 3:00pm 'FALL2009 7. (6.+4+5:15pts.) The graph below Show the: rate r(t), in hundredjsof thousands of
galions/hoijr, at which water ﬂows from a dam, where t is in hours. The water'begins to
ﬂow 2.5. heurs before midnight every night and is used to supply drinking water to a
nearby town. E 2 = .
b) To estimate J'r(r)dr, ﬁrst draw rectangles on the graph above correspondi " ' ’ e
0 MKH right—handgun: Where 72 m4. A’QS i 6
m “M “1 er {QM (m '3‘ W “6*” WW 2
0) Estimate J'r(r)dr by calculating the right~hand sum Wiﬁm = 4 from part c. ‘“‘
0 . MATH 124 EXAM III 3:00gm . FALLZOOQ 8. (10pts.) The ﬁmction h(t) given in the table below represents the change in height of a
given tree, in centimeters per year, where t is in years since 1980. If he height of the tree is originally 200 centimeters n 1980, ﬁnd your best estimate for
the total height 0 e tree in the year 2000. WW ‘ 33; j g (I ngLHSJfé‘)
rgﬁmb
3 (I5 e a SUI/592343)
2” S “I: mo 2;
{$me “e”: UM Avg =2: I Be m ...
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 Fall '09
 GIAMBO
 Calculus

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