MT1-1 - METU Department of Mathematics Calculus with...

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Unformatted text preview: METU Department of Mathematics Calculus with Analytic Geometry Code 3 Math 11.9 Acad. Year 3 2009-2010 Semester : Spring Date 1 April 10th 2010 Time = 13:30 Duration 1 100 minutes I‘ll-II. SHOW DETAILED WORK IN EVERY FROBLEM. Question 1 (8 13135.) Find the following limits. Do not use the I’Hospitals rule! aunt—MW ; [Mn S‘Enx h ,C K M i kgcg X Ku’L’Ofi} “7;— ‘A ”“- Question 2 (6 pts.) Find the equafaicn of the tapgent line to the curve n: cos m+siny “—- % at the point (1r/ 2, W6}- rflwg‘ 7'31} (5,! ”—2. [email protected]%+~xflvamgygfij /'_,_ 20'th WCCJSX 3 I (£233 m: %3§N}:m% ‘ z I - ML 6 I 3 z, "I?!” 96’77L6/w f) 3“]: _., ”T" I If ' '- ' 6wfflk”a . Question 3 (6 pts.) Let y = y($) be a function of x. Find 3;” if 2:2 + y2 + .1: = O. '\ | ' _;__ ”1 3w“- ZMQw’MW m) 6': 12f *3“: Z+2w”+%a) O --> 37 “3% it“ «:9 3”?“ “f“ “4%“ x m MW in“ ‘ 43% “‘ f 3 < 1 Question 4 (3 Pts') Lat fix) 2 { Zx+b :; 1 G? {:5 C9471? {xcppf @331ng (24+ XSL a) Find the relation betwaen a, b and m for f to be coritinuous everywhere. Fwd kw 10) Let f be as above If f(2)== 4 then éetemfine the value of a b and m for f to be difierentiable everywhee. fl§):é 5'37 Zonb: r I“??? flaw-3 (#le {M 759% a if “‘33”? L3 3 \L! (V \r ,LE 3 Q9 3 m 3; ii ‘6“ “3‘ n N QUEStion 5 (6 PtS-) A point is moving on the curve $2 + y2 + z = 0, 14:5 $~COQrdjflate is increasing at a rate of 1 (32—: m 1) at MEIER the change in the y—coordinate at that instant. . ,— ? ' ,1" ”"9 Question 6 (6 pts.) Usilgg derivatives find the point on the line segment 2:; + y = 1 (0 S 37 S 1) that is closest to the point (3,1). 92:: (x-m3frgwf x lxiémat 4):: ; ’ggaggfl Question 7 (4 pts.) Evaluate £—( [$12 cosztdt). a? MEX (£31262 m... Question 8 (4 pins.) Evaluate the integral $715511 2x + 9:3 — 5)d:1:. Question 9 (1:? pts.) Let flan) be the function given by Til-23'. 3.) Determine the asympiotfis). {xi/77 7pc“) 3: :09) X31. Tris WF{ @3174: X7217: {fa/205%); o g :0 r15 £70m 053m b) Detemfine the intervals of increase and decrease. ‘ < O of; (/21. {2.1; 2‘ ".376“ ~--—._. ,J{O77~:.~.— 477%{017‘ ...
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