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**Unformatted text preview: **MA 113 '— alciﬂus I ' ' ‘ ' ' Fall 2011
" ' November 15, 2011 Answer all of t e questions 1 — 8. Additional heets are available if necessary. No books or notes may be used. Please turn
off your cell ph nes and do not wear ear—plugs during the exam. You may use a calculator, but
not one which as symbolic manipulation capabilities. Please: 1. clearly indi ate your answer and the reasoning used to arrive at that answer ( unsupported
answers ma not receive credit), 2. give exact nswers, rather than decimal approximations to the answer (unless otherwise
stated). Each question i followed by space to write your answer. Please write your solutions neatly in
the space below the question. You are not expected to write your solution next to the statement
of the question. Name: Section: 13—8+3+2
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(c) 111111625672; :L‘—-nr/2 1 — sin x ‘ (a) Find 1: lineaﬁ'z'étion 6f = ﬂ at a = 4. H 41¢ ) av, ‘ «Ma/H may) cvx—aﬁ ‘Find the" solute maximum and absolute minimum values of the function = 51:3 — 62:2 — 153: on the int val [—2,3]. ﬁll/cm) = 308—152 vx ~15 —P’Cw<) DNE? #10020
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(—aP-GC—aﬁ—wm) = —5 — a++30 :@ 3 33—GC‘?)~'+5= 37—5+~+5: .7“ The absol e maximum is .— 9‘ at :1; 2 N a & The absol e minimum is __—;7_l__ at x = ' (4) Consider he function. f '= we” on the interval (—oo,'oo). (a) Find t e interval(s) on which f is increasing and the interva1(s) on Which f is decreas-
ing. 'P/(J/X); VX6061“ eW' I = e3”C 006%) 6% (“ﬂﬁd ﬁw
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(c) Find 6 point(s) of inﬂection of the graph of f. Show your work. (a) Interv (0) Point s) of inﬂection 7 (5) Fihd tiiv'o ' ositiVé numbers It and y whose product is 49 and Whose sum is a minimum. 3% 7
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7 (6)~ A canister is dropped from a helicOpt’e’r 490 meters abOVe the'ground. The canister has
been desig ed to withstand an impact velocity of at most 100 meters per second. (a) Given he equation of the acceleration of the canister as a function of time t is
a(t) = —9.8 meters per second squared (the a celeration is due to gravity), ﬁnd the velocity v(t) of the canister as a function
of tim t and the equation of the position s(t) of the canister as a function of time t. :— "‘, ()30 n MW
(ti i8£+c V0 wazjjg‘ca d =>o = ~7,8(oH—C¢? C20
vLJc]: “7.8%: sUc): 4,83%, Bwi— 5(0) 2 H“? 0 79325470
a >5Lt) = ~98? + +70, (b) At W t time is the impact, that is, when does the canister hit the ground? h? ‘HO m€¢f€[email protected]
h x
5<Jcsea+3=CWO = “3.8 ’93 ++70 g Can (0) Does he canister survive the impact? lap .52 440830
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(b) Time of impact: t = l O I M69 (c) Does the canister survive the impact? ' ‘ (7) Dbctor D o'fenschmirt'z is shooting hiS'nem'es‘i's Perry the Platypus out of a cannon. He
‘ 'wants‘ Per y the Platypus to land astfar away as possible; The distance to the landing point is gi en by
f(0) = 450 cos 0 sin 6 WhereOS 9 Sv’Tf/Q‘iS‘ the angle 'the‘cannon' makes with the ground and the distance is
measured 11 meters: Find the angle? which maximizes the distance to the landing point. 41/(6): LHBO Cygfyza + +505([email protected](—Sm0) -:_ L{'50 —$ma(9). _P/(©): G DIVE/7 ﬂmh egg: iSma- Per- 0365 W/a) 4.9,}? @dm/ﬁ
Momme @(E) can [Men/a1: Jxedc endPIISd‘ (8) True 'or Fa, 'se? Circle the correct‘answe'rs below. For each' correct answer, you will score 2
points and for each incorrectenswer, you will score 0 points. You do not need to justify hm Lac) 2 km gen/(x) — f($)g’($)_ HI 9(13) H1 (9073))2 ...

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