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Unformatted text preview: METU Department of Mathematics
Calculus with Analytic Geometry Code 3 Math 11.9
Acad. Year 3 20092010
Semester : Spring Date 1 April 10th 2010
Time = 13:30
Duration 1 100 minutes I‘llII.
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}
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' ' 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“??? ﬂaw3 (#le {M 759% a if “‘33”? L3
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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.
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”"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:: (xm3frgwf 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 Til23'. 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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