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Unformatted text preview: APMA 111 Name KE’ 1 Exam 1
February 20, 2008 Section Write and sign the pledge: Directions: You must show all necessary work to justify your answers. Solutions will be
graded for accuracy, completeness, and clarity. No notes, books, calculators, or other
aids are permitted. Please circle your ﬁnal answer. Points Earned l) (20 points) Evaluate the following limits. When appropriate, please specify either
—00 or 00'. J,"
nx2 L ‘9‘ ‘ 3
a)lim(l ) : hw iii/TEL: ': LIL“. 71.9.11: X—DSO x 593990 "’ x—‘Pyo X
L , 1613
: inn T
ELFV00 "'
a.
3 iM T t: E 2) (30 points) Evaluate the following integrals: a) szrdx la PMCS’. (Arm
(hm AN 7—1160»:
V “'7‘ 1“/51sz 5&1)qu _A_ (566
$(19‘ﬁ325‘ $L+°i e) I:(:3f;'dx mm W6 a==r>xL+Lx+t =AC HMCEFQX
X==n ﬂ i== MAdPA': “17%” igAJﬁgMai )JWtzgc
LSé—M ggrﬁ 934M}— "3&3: “wwﬁMmb
/+34p»(1g)+c 3)(15 points) Find the area of the region enclosed by the curves y = 2 cosh(x f 2) , y = l ,
our solution must include a sketch of the region. . f @6415 4) (15 points) The halflife of plutonium239 is 24,360 years. If 10g of plutonium is
released into the atmosphere by a nuclear accident, how many years will it take for 80%
of the isotope to decay? FW‘ mt mt Plasma reweéw’g Qatari yang,
p(o\=l0 anal PC74(%°3a5. [Aft 2413630  k .L Llﬁm k. 9697408, >5>6=l09 “=‘P9_=e, S) (20 points) Consider the function f (x) = e"(e" — 1). a) Identify the domain and x and y intercepts of y= f (x) ('DOHMM G— as Do)
(WT—Oﬁvqﬁi T3 65:0) outY W‘ \f"chG/Ce (53"..0 —o==Dc3 Kﬁi’q’p—‘g‘l—o b) Identify the hOrizontal and vertical asymptotes (if any) of y = f (x) . u». my: 'aééfvt): com; we, MG: 42365—31320
)Q'W K4557" ”Di—5&3 “Bl—Mid
0) Identify the coordinate;K of the relative extrema and inﬂection poi
41A: 9‘69} 43"‘6 waitéli mate," ——3 13x4) it? 1,
,_ —» 73> $9» = ~ 9M. 15611me
i 0‘3"? t 16K ( :0 a: 2' K Mariam. $“(x\=£(zéké3=4é"d‘ =1», @é‘ ) 1“e9«11=1“<1nau’ae%1 We We as
,4? M Mm @ )L=*Q.m2.o—V\A'FG'9J\L\9: 10.43:: .ﬁ: ﬁlmmowmgo ER (ﬁre1 NM; FQML [’44) H '/,—'~J—
‘F (A'O 7:96 KGQBKABDB ”’D’isaviﬁ’e/K =Aei¢x=—Qh4 .__. + r K “T ¥=—9M’f"
.. 4s .1 wc—w @
Wei («95 1 (é "9‘5 "M' “”43": 51.33 bierl 41¢, (1) Sketch the curve, y = f (x) , plotting the point(s) and asymptote(s) found in parts a  c. \ I” 2 ex (Lexi4) X" ...
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