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Sol-165E3-F2009

# Sol-165E3-F2009 - MA 165 EXAM 3 Fall 2009 Page 1/4 NAME...

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Unformatted text preview: MA 165 EXAM 3 Fall 2009 Page 1/4 NAME GRADIEQ KEV 10—digit PUID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. Write your name, 10—digit PUID, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3 and 4. 2. The test has four (4) pages, including this one. 3. Write your answers in the boxes provided. 4. You must show sufﬁcient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes, calculators or any electronic devices may be used on this exam. (9) 1. Find the absolute maximum and absolute minimum values of the function f = m3 — 3:132 — 9x on the interval [0, 4]. (m :Bxlméx * 9’ C59 / 2 w a , MO (X3220 1 x damage ——->{><.3> (Mi)... 1 g X3?) WI) ~1f/Amofuw (0)6?) @ Ho): 0 I 8(5) :27W3.f9_9.3:w2.7 abs. max. f(0)= Q “pr—ea w‘S-lém 9e :2»??? abs. min. VG) = ~— 2 7” @J IE1 (9) 2. (a) The Mean Value Theorem asserts that for the function f(:c) : sina: on the interval [0, 27v] @ there is a number 0 in (O , 2W7 Sin ‘2 Y7 WSW) , \ /....V./WW.<M= a: m mm,” as”, . \$— Z1”? y ‘3 " (b) Find all numbers 0 that satisfy the conclusion in (a) 51(6) :00 §%)\$n C03¢30 warn? ﬂﬁﬁy such that £5 ,(C wry w m '21,? MA 165 EXAM 3 Fall 2009 Name Page 2 /4 (30) 3. Find each of the following as a real number, +00, —00, or write DNE (does not exist). (a) lim sm 4m (ind 3W4” E? w (ﬂ. mpg cc—>0 tan5a: Ewafo E“ gﬁ’abgﬁ g 4 “,9,” WW 0 g ‘ _ L H r We' (b) lim ﬂimw lam W73 ._, 2 m 00 w “3&0 123x ’l W «'3; .6 a, we: (c) (1 — tanm) sec mm (gim- 2121,r/§3;}XQC§ mam a L. b Ami; < (d) lim sinmlnxzz 9mm 35")?“ m ‘ 3360+ no War neon WWW a. “4% (—0—? A MW e. w. 1 . o e:- n “KwrQJF m: “7'” \$2 ("ﬂ I 00311: L H Mm (e) m—>1(r—72I51)* 1 —— sinm \$4 wig E 1 2a e» 4 km?” Q @3057le (i + +3?) (f) lim (1+ —)7“’.::: "m 6 ’ :3 ~ n . W7 ,7 , , :3 W? W“ 2? x t < e 2 9 E37 Li.é . 3’9 (“\$51) 71%, 4%: m7 5} w Kg W 3: / V” 1+ k-WWAW ﬁner)“ m Waxm a .3 , X (“i y: (6) 5. 0 is a critical number of the function f : e“l"3|. Complete the following gm ‘xmm ‘ ; f’ is positive,@§e:i£e) (circle one). @ (b) If :13 < 0, f’ = ; f’ is negative (circle one). (0) \$1933 a , (local maximnnl: ocal minimum, neither (circle one) MA 165 EXAM 3 Fall 2009 Name Page 3/4 1 (16) 5. Let f = Give all the requested information and Sketch the graph of the function on the axes below. Give both coordinates of the intercepts, local extrema and points of inﬂection, and give an equation for each asymptote. Write NONE Where appropriate. 3; , 2 W WW Dom“ (0, 057) , > Inimﬁg/ W / (ﬁ/ ‘53 g, {éviﬁ' ', ("g x» {mi . ' Huh» Z m» r, tar l i» wig/W 21a ' raga (1,07 :: symmetry[ N G N I l l bl ’9 V V ugzw ﬁt} : Myra? “a”; W horizontal asymptotes 23 0 t gm «an V i rag . , O _ vertical asymptotes % g Q gm (lighters m, W P» Q {E X intervals of increase (/0 If lmmma‘ / "‘ g in “7% intervals of decrease L ) local maxima local minima intervals of concave up points of inﬂection MA 165 EXAM 3 Fall 2009 Name Page 4/ 4 (12) 6. Find the w—coordinate of the point on the line 61: + y : 9 that is closest to the point D : ﬁlighiwpw 0;) m {%§}ﬂﬂ Hawaii—m: i’vovaqzm? a? @mﬁsagﬁ' Mme/rm: was W Dr: 'X-tggﬂ" chi/2;” ., ( w) (“A t) K o 2 4 “K m wing i, [Q (n+3) +2; (saw) (me)? Zmaﬁwéeéﬂ' t)“; f ‘ ‘ ow 90 4 (12) 7. A closed cylindrical tank is made from three meta{s7lieets (top, bottom, side), which are welded together along three seams, as indicated. The volume of the tank is 1000 cm3. Find the radius of the tank so that the total length L of the seams is as small as possible. Weak amen h :_ more “IT‘me @ J L F, was 0 < T < as ‘2 MTV “*5” #3:: ) AL V 2009M M" r: W "’9 W3 Cl)? ‘TT‘Y" a dim mm m 3399 “a é 2:2” 1 4T? "’- Rﬁﬂ :0 “my ‘f’ an @7133”, \EEWZE mmw 0 we at»? wee/erwrrm‘ﬂ , , 47”,»1?‘ di” :10 B \Kar‘sﬂ” i“. Pm o n (6) 8. Find f if f’(:1:) = 2c0sx+sec2 :13, ——-725 < x < 127-, and : 4. Mg; ﬂag? xgngwﬁz ism “EMT a WE; veg We: 4*, ME ﬁx): 6(er «4m “Coma -+-» 4mm2f7§§ ' . (a ...
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Sol-165E3-F2009 - MA 165 EXAM 3 Fall 2009 Page 1/4 NAME...

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