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1021 quiz 5 A Term 2008 answers

1021 quiz 5 A Term 2008 answers - ANS WE Name K E Y MA 1021...

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Unformatted text preview: ANS WE? Name: K E Y MA 1021 - 2008 A Term Section 2 October 10, 2008 Quiz —- Sections 4.4, 4.5, 4.6, 4.7 0. BONUS QUESTION: Circle the gp_e correct spelling of “ASSYMMPTOOTE” in thlS QUiZ (hint. It is NOT on this page). (2 points) acmnmcirclcmmmnmspenmg:ircfinganyimomspeungswin imalichl: this offer. New valid where mohlbiled by law All decisions on]: professor will be final. No ash value. Please mad and follow all army insmrcljons Not intended as a llolalion device. . 16—36 Mulfiply nummhr‘ “Ml 1. Evaluatethe limit: 11m Aenowundw by "lh—c ConJU3‘~le) X916 4—\/:C 4:: 6‘9“: 'Hne final-that Please ShOW your work. (5 points) [64 (444; —_—. (lg-x)(‘f+\f>?): off; 74.x xgsrg ‘f’fi 0+5 lé'x fl-‘X ‘ llM [A ': llIM 4+0}: .___ 8 Answer x-‘Nl, WW X319 . . . x2 -—9 2. Evaluate the I1m1t: llm H-w x + 3 Read carefillly. Please explain your work. (5 points) - Cl X7._ 3— llm X. __ llwx __.._ 1m“ T >< - x—>—ao X“; “0° x 9 ‘00 T." X >6 3 "V“ l + “m E’. I J“ 5; Xe .00 "" “"‘ X Answer Fr ~00 -- O .— 1 on m 00 3. For the function: f(x) = x4 + xlnx 2 Find 2 Show your work. (5p0ints) dx \ 3/: "lfij'l- fiwxi- ¥(;)T fogf'fi“><+i // ( ___ 2 ‘3 r 12X+~£ Answer |)_ Z + i K X 4. For the function: f(x) = Sin x Find D300 [f(x)] Explain your answer. (5 points) I: 603 )C 4L, ‘3 EvarJ “i ai-Qr'u/A‘hv’t \PE'h-I'rn; a” -:. ——5|:’¥ )9 y“, "H ‘H‘Lfi Of‘t‘jl-krgl _p’fic’ha'fl} W E ta!” -: ~Co5x “”5 oi _._ S!» X Hun (01m 2': SIP-f) x _ #3 Answer 3 F}; k BONUS QUESTION: What is the first letter of John Paul’s Calculus name today? Y [j 5. 5 3 x x Consider the function: f (x) = "5— — g a. Describe its domain. (2 points) filo r 2&1 nomb—zrs b. Identify all its critical points. (3points) “f ‘ '2. 7_ X z "' J Mm ii“— 2: x (x ~I) a o .S' 3 _ i ‘ c. Use the second derivative test to determine whether each critical point is a minimum or a maximum. (7p0ints) t I! 3 2 Q/x)=4’X-2X= 2Xf7-X-Ij I? i i F (.4) .; __2_) (oncave aiowm) X7.'-I I; a max :j ,C”(o) n, O Omani ~[—eli ) X: 0 could .191 mm) ) Win .r of IW'PI'ef'ba-q P;V\i->K *Am‘lnflr kj‘fmja aloe; Mdlcék X110 IS an inFLQC'fiSQ foli‘f. il 6. Be sure to explain your answers! (9p0im's) Does this function have a horizontal asymmptote(s)? If so, describe. If not, explain why it doesn’t. N0, SMCA Ill“ Lflg) 6nd hm "p/K) do x»+aro xa-as no ‘I‘ CoflV-erje +3 (‘— f‘eml hum [914‘ Does this function have a vertical m explain why it doesn’t. (1)25 SM“— [\9‘“ ”F00 is Uhal-e'Rne-J) Hm“; ’ x—>3 Grmspoair ”in c. verb“! 645),“;le al- 16:? ,3)? If so, describe. If not, Does this filnction have a slant assymptote? If so, describe it. If not, explain why it doesn’t. Y2}, Since we Lave a iuaaLr-ah} «shawl-0...! 5; G- linear ”R’V‘O’htfi ( ”kge/‘l‘mae 5F OM ) Answer each of the following three questions about the function shown below. , d. 6. f. Find all intervals where f (x) = x3 —— 3x2 is concave down 566 (pork above Answer (”05 l) Find all local maxima and minima of f (x) = x3 — 3x2 Find any inflection points of f (x) = x3 - 3x2 Cfimlgl ) fl Cle-fit I‘n (mm/exl'b mi“ [2| mallard-e; an ln'FlEC'll'aan (admi- (1,00) v g. Sketch a graph of f (x) = x3 — 3x2 Concave Ohm-”W Caner—we. V? IIIIIII IIIIIIII IIIIIIII IIIIIIII IIIIIIII IIIIIIIII IIIIIIII IIIIIIIII IIIIIIII IIIIIIIII IIIIIIII IIIIIIIII IIIIIIII IIIIIIII IIIIIII'A’ I‘IIIIIII IIIIIIII I‘lII/JIIIII IIIIIIII IIMIIIII IIIIII'I IBIIIIII IIIIIIII'AI IIIIIIII IIIIIIl/II IIIIIIII IIIIIIl/II IIIIIIII O IOCfi-f “AD-x) (Def [Aida—CV? 0 1 ’2, ”—‘Lf i0 (4.! Mtvv 3 8. What are the dimensions of the cheapest cylindrical container which has a circular base, no top, and has a volume of 3211 cubic feet, if the material for the side of the container costs twice as much per square foot as does the material for the base? (12p0im‘s) V: Tiff-2% 7‘ 32W in: 3.3 C(r\’— \Z‘frfia— 'lTrl F (Wu: ”11%W—l— ’Zur ”‘Ll C”(r); O v-Cor 5.0} r) fine 45% Alva; CfHCC-v-e up) (LL-f I) ‘— Mmuvivm b-«Eta ‘1 BONUS QUESTION: The following function has what is called a “quadratic asymmptote”. Give an expression for the quadratic asymmtote, and also determine its vertex. 3__ 2 1 Q f(x):x 5x :5x+1 '1'“ x —Lffl+\ _+_ Kt; x.— 9— W X ,fo+\ 7’ X3“5X?+$)‘—rl 9,; K1— LHCT-l M x2— x’1 - -“fo’ L '1 X4.- x~l Veflex (9 2le *************** END OF QUIZ **************** ...
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