=========================preview======================
(MATH301)2001-2008_math301_midterm_sol.pdf
Back to MATH301 Login to download
======================================================
200~ ~l tl+e.t'~ ~olc.(t..s_
CD (~) 1)~"-ft F: ~"-=, ~~ Gl;Wer~J:a.-;{t;.'J'.'/Q~
(...)'O.~f:~"~~~~~..f:..Ua
~it-=(-'" ...,a~) etlC:..'" .
(c.) ~f ~ (tt..., R. ~ Felt,':!J'" ) 'If;:~l. of (..,':M(o,<.t 0 cf (IC.))., (0,..). Is r=~.u... 4 (0,0) ~ .(f,o) ~
~ C ~':l ~ '\t~ ~j
~ 1M.~'l.f.r e -~"'A.('\Tw)= e ) e +we -:=. -x . s\'w ~,t nt""f'" (.,..~,.,.., w \ __ (0.1/)-\) J (Kt'j) c., ~ ~f('esse..l A' 4l ~e~~"c.. ~~cf(""'~)' ~"d. ~w. ~ ~(T."I) -:::'(0)-').
~ 0 t\ U_,r 00 c-nt<
.\71 {tWc, J. ?( a. '~~&G)t! =Z .... ." c-.
o ~ tc:=.o liJc..t')~("k~2.t~.
S6L\ GC"e ttC..,,'t ~ ~QA\ ~~~,t k-(Q,,-LA~+:t-Q.... )C() tr..... (Q,,-4A+')=#'O.
""'oa I "'....
~n..
(10) ~ltth\ba ~~J~IOO(Q.i2.aM7QM-&):~.(,) ~tO". l\M.S~ (Q~-4,,+\) ~D. '
Wl" ;
(.;) ftWt. li"'_'..f (Q,,-a....,) ),0. F;..J. ~...(Q,,-a..~J
200R--Mi,t.tfe(N\. ~k~
~13 &,"'. tra~T: II"....... IR-~J.'f"-.t
fk.1IA. \l f6d -f(....)-1T~-cJ.) \1. '=0 ,
'X~CA. (( K-~\\
(b) .3 Bfct,r) ~\4.cA.-M-VL=\,o"J~.1 j==fo.oJ'" J
J
~~At ...\( 'PDl..n .J 'B(~, r) ..oJ. i'~~"14S
oIeJ -1 ~"'.
(e) ~... (~.. ), F(",o):o, FCo,'j) co ~~(6,O)=O
~(o,")~. Tc;J:Cc o1 [;}=O.
~ IIH"''1I-fc.,oFrr'''1111 ~-, I~.J,
(~p.l,wt' ,\ It&. :=. ."t.......'L -CoS8S,"-,8i 2.. *Q
'Ynl,c", \ ~ ---~ . " \'J ../'
. A (O'4.~ ~-::. X ,
-. F i'> ~.~~.tt"(p,.). &=~. h..,. (1,0), ~e..,. (1,0), _~ l:: l.~')(( )'= ~ ~... -K~i(x~'le.J z'(I.'X,) ~" ax x ~f, :t. i(\~ ':ta..
T.t. L)Jf&..
=~ }
gr-=-"'1-'ii. _ l)f.;t a.t"e C(J.."i;"'cw.tftt.S.
1
a~ ~(~)-(K.~'1..))/& .4~ F \s c( 01: (,0). ~~(\~O("-) f",~ ~~.{(/O).
~~
\'
I
-o --
-t
-GIl
-
-
-
\' l\ I
o .-...
~(...) ~rst f~to 3&t ~Q...\ so..d..M-. a.) C,) ~~ M... ~-...s.r (1:"-41",,,,) ">0,
Vl~_
A'"-2.Q~",\ .Ie Q M z..'= 0 -t-(' -.u W\ --l, z., l, .It
.
\J.. -t1',) -to Co~ct ".~td~ -f {alit
~ ~~-4"ot't '= aM' -a",1:2. f~ 0..\( t\ l.. I. ) ""~\I +.~. 4.-G~
~') ~a11\\ \s ~"-tt~;~",~t,'C,. ~o~t"ess~ t'" t"'K-2.Q"....-a"...z.. --0 M\eQ.l4.s ~ -, II" ~.,,"" Uoft"~d
\'~ QII\~ n... -,kfl\ i.l,,-2Q..t'(~ ~-tZ:= ~-2.C~-(1)~(",~1 Vf.>o 3 N<=-tJ ~~ . ==0 . ~).tJ ~ ~"'-2aA",,+tA"4:I.)-o\ <f.
\'_(a..-z,Q..ot',-t4....""l.)=O (,.. In ~ "(10_ ( , :\ J
~"'OG J ~fIII\ ~""""-"""""'JI: ~"'",~)=,
~aK-2,q....-t'c -tQ~,& <. t
"''''00 ~Od ...
o.
~ q,~-a...,,\,( -2. <: aM, -t.l"'ot'2..(') W f. do (c.~) fit'S-E: .
M.c,-:: Sf f1:1,,-0"+1 : "~k~ ~M
COtl\4Si'J.Ct' bf'\,-':' -(1".
-..( M e .c ~"M.rfCoeore...
1\fM.. \~~\ ~~ ~ bi\~ b-t.w.4J
3 a"IC.-a"IC"'" \ CcsM."e~~ ~ M.
\~rQ.~-~+~)-:.O ~ (c1W\ C.bt\~+t-+"~)=0
.
Y\""~ ""....'"'&.. -a N'/ON s;..J...~ I< ~N'~a.,,-Q E(~ 'M)
. ~ ~t ~)~
V\........ -f "-~ ro:;... "....X(N1 N')." we."-.ve .
.......=It....s'':' -eel"-;..",) ~I~-Q..J Q",,*,-a"Itt2. '> Clot.. -a..~,-~ '> ~_t
.1\......... II\"~ a. ct. :. -\r.....~(~-'l....,) ~0 "'t-lot.. -~1')'"-> tt"k""'-~"'l.."., t '. ~-1.'-". ~-2t
~....~ ~ ~ a.. -:r I,.
, ,
\Je. ~G.v4. .
. .
I1l1l<-k~-~~Tj '> a....