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Unformatted text preview: PAM, 200% Pwm, (3.ng 2 1. Find the following limits (5 points each), giving reasons for your answers. You may use
any method from this course. . VaHZ—x/ﬁ ——L
Liv—*2 1r —2:r
a ' W1: '53; 5?». +57; Q: +2)—1y. a
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oval ¥M(mmo 7. (14—1.) 3 _\
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:: “LL—S— 3 2. Find the derivatives of the following functions (7 points each). You do not need to simplify
your answers. 1
a. If y = tan(3:c2 + c) then — = 65L 51.94, (gk2+e> 9%: = @hzﬂk‘mv‘ (GK) :2 1,
b.Ify=eﬁthen:—y= (KPH)
3: x.— I34 ~‘R
ﬂ? — (ﬁfe §:C%. =93“ M , : £23" 4 3. Find the following indeﬁnite integrals (7 points each).
1 ' __ 3
a ft? —t3m= we we we"
we 45"“
you = '% 4"” ' : r V'“ C,
Swat’gJ“) 38 W k "r r gt 3;”. [It’N’C/ 4. Calculate the following deﬁnite integrals (7 points each). a. f3 In?) dx = HQBW Uni?) 5” b3
My 5 3'09“ l 3; _ qwr—w‘)
duiw I, L ﬂat 2’
'¥
2 lla
b. mks—1073:: I
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n.
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.r:. :JI iJI'IiII‘LH lie“mun” LJSII' :1.Pl_'i'. under [hr graph 43.1 ‘I':_.__: :r: — ._'._3_' [J'biun _,_ _ H 1_.'. r — .[
II:ll'..'l :‘i 'JIIIIIIII'L' illIll"! .LlJalltmlmMJlIJL I~"I'l.ll.p.:1 .thl hprhl rudimuﬁg. '1]... "1.1.1. ....1.. IIH”;
.uEwnr :n: r: mun Tuu wﬂJ mamm: 1m :rulil I—nr I."'.T.1I.‘:.Iil'.g Hm: jnchmI {WuEU]: 
a'IpJIrmin'lmlh "will fr. 117: nII1IIh "'IIII 1.III:'L1IIJIlIIHLHf1'111III1.;.I Iml: LL'. ll';l."1.l.ll'".'l_'!liﬂ3l'_1'.hl_'d I:_'..'
Trllllr I :y'! 2.: HT 1hr: paint 9.2 H .1_.‘.' rumIr. I‘fi1l.‘lr.!'Ii nape:"iflning HuiL l'uu u. .urnlatrﬁllu " mua 45113‘H5n31a' ‘ CI 3.51.4 4 {EEB' + {is133' '4
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an} n a '1urm ﬂ" '5 1II'.I'. :I‘rlmi itnll '. [:arIH'I'.rIIrI2.ur In :: '.r.:llrll Elm T 7. (14 points) A radioactive frog hops out of a pond full of nuclear waste in Oak Ridge,
TN. If its level of radioactivity declines to 1/3 of the original value in 30 days, when Will its level of radioactivity reach 1/100 of its original value? Note that this is an exponential
decay problem. RH?) : Ra Q: ht 4230 'LR/OL‘R/O‘Qr MGF‘W“ 'QuBS h = It?)
30 8. (14 pts) Let f (3:) = x3 — 12:1: + 5 on the interval [—5, 3]. Find the absolute maximum and
minimum of f on this interval. Absolute max: ‘1 y . f’rm 3x’z'l7r = goo—v) Lillyvso k:i7’ 8 9. (14 points) The graph of y = 9(33) is given. a. For which values of a: is 9(56) discontinuous? Don’t worry about the endpoints at —6
and T in either part a or part b. b. For which values of a: is g(:c) not differentiable? 9 10. (14 pts) During the summer months, Terry makes and sells necklaces on the beach. Last
summer, he sold the necklaces for $10 each and his sales averaged 20 per day. He also found that for each $1 increase in price sales drop by two per day. If the material for each necklace
costs Terry $6, what should the selling price be to maximize his proﬁt? Tmhfmq.?,30 mmeaw
M mm my 395;,“ 200°: Mam. reverbue Cost M M
P —: (lomM'LoIA ﬂ, — Celloiv)
F; Ly) (1011:) [LtJrﬂl—zMUH'ZO'erl = has—2», ragQ»:
1: 1'2, "(x P'ly) = 10 11. (15 points) An open cylindrical can (without top) is to be constructed to hold 16w cubic
cm of liquid. The cost of the material for the bottom is $2 per cm2, and the cost of the
material for the curved surface is $1 per 0mg. Find the radius and the height of the least expensive can. (The area of the curved surface is the circumference of the circle times the
height.) h
2 _. =L£_
C: zar‘ntrh V"‘9"7‘“"‘° *7 1" rt
It. _ 7'
G 2mm zed—1%) ~zmz+wl7 *ZFD
.. i
I L:
C Q'ITEZ‘P— rm] “L
[.9— rgax r'
W QV: If,” 11 12. (15 points) Use linear approximation or differentials to find an approximate value for
3
8.5. aw is) a: 1%) mm (My —2
“8‘5 livmeﬁ “MEWS55°) W53
'1: z+£ll~1>55> = Z+£Lﬁ 5% 13. ( 15 points) The altitude of a triangle is increasing at a rate of one ft /min while the area is increasing at a rate of 2 ft2 / min. At What rate is the base of the triangle changing when
the altitude is 10 ft and the area is 100 ftz? I , 2/oo«l
([1; 20+ '2 2 Z__/°_o_
cQB _ no
__((o=(0'aTc = 4/0 Z 2 _/60 100 (90 12 14. (15 points) Sketch the graph of the function f(a:) = Bil/(3:3 + 8). For this function, ":0
maﬁa"
N N N
Decreasing: G h) *1) U (—1. , 0°)
1 n U n U
9.0»ch ~H—F— ewwmw a, ...
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 Spring '08
 NOONE
 Calculus, Trigraph, Terry, 14 points, following definite integrals, mun Tuu wﬂJ

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