111_test1_key - APMA 111 Name KE’ 1 Exam 1 Section Write...

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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 ELF-V00 "' a. 3 iM- T t: E 2) (30 points) Evaluate the following integrals: a) sz-rdx la PMCS’. (Ar-m (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%” igAJfig-Mai )JWtzgc LSé—M ggrfi 934M}— "3&3: “ww-fi-Mmb /+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 half-life of plutonium-239 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 PC7-4(%°3a5. [Aft 2413630 - k .L Llfim- k. 9697-408, >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) out-Y 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 (fire-1 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 bier-l 41¢, (1) Sketch the curve, y = f (x) , plotting the point(s) and asymptote(s) found in parts a - c. \ I” 2 ex (Lexi-4) X" ...
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