Math Quiz 1 2009 Key

# Math Quiz 1 2009 Key - PTFE 8893 Fali 2009 Quiz Math...

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Unformatted text preview: PTFE 8893 . Fali 2009 Quiz Math Skills (25 points) 1. Evaluate following; 1‘ . £1 .0, V" p. . "" , . a. , jdX/(l +X)2'0 = 21—:19 .— a + C’ (2 pOints) LA "2- H- :5 %/ . , f l ‘— i ‘5‘“:‘4‘ :-—{/7L>Q +5 \ . 1 .- ‘1— 1; 5 b. Idx/(1+x)1-°= f a” a ... jMM ' (2points) La: Hvﬁ A5: 7* C£JL ' c. Jxexdx= (3 points) , 3 A ”My 6%.»?va 19/; WWiﬁ/y’ I I II i'2._ Solivethe £01.10Wingdiffereritia1equaﬁon; ' I. I -- I (6 Poms) ' ' ' da/dw-e/ws ' -- . With the initial condition that B :90 (a known constant) @t = 0, and T is a conStaﬁt. I ' I i '- UJ_ ' Soilvé the fﬁﬂow differeﬁtiéi_equatioﬁ-Witﬁrthé bouhdary cohditions. that are spemﬁed I _'_ ' "I (Fiﬁ/ck;2 ; 312 IT. where-28 is an uhknéwn afbitrary'iaositive ICC-3113mm: BoundaquOﬁdﬂknm; _ ._ ;-1.- : ' _ _(Gﬁbﬁﬂ®-._l Iﬁ§Whmﬁ=0,T%0 I I I. I I _ l' b. Wheﬁx=L, T=1' iii-3’!” -; )17’3‘ a -~—---+- *r we} x 7'”- '_g-”. 24-2 'f‘)‘ " L: O ' ’ .LN _9 '--+//c. ' ' ' . ﬂ :3 {If}??? " I 5/2171 #A/L, [Mf/k/A “—0 ' K >( ”'7: AWAXLMB’ SM, 2% f #10 ,5 EC :7— - ,3. ﬁzz-:0 69” ,9 ,3 mfg/w We?” >..,..._.-... .7. __ “‘7": 8§&%V\K 7” i“:- i “'3‘ . 3 W ”MW/M, ' (Mg—w """"""" “”"d/ S M/L/Kklé _‘_;4.'_:j_s_olv'eth§f¢11¢wdiffeiemial equation with the boundaryc-Onditionsfhataré specﬁﬁedf -_ 5 7 - - "7-?d'(rdT/dr)/dr=9 (6136mm) I‘ Boundary Cohdiﬁons: I I I I I I lla.IWIh‘enr=r1, TII=T1 _ . \QEIT ..+ RN§+ i, . . 850.0 3000 .05 ,00 08.8 .5 >00 M0. £00m E.- 10% _..m.:0530_m 3.0 . wﬁwqommotoo 0&- mb 200m . 23%» 1x +. ..+ 7.x 0‘ N0»... aﬁ-=~00+§~§03§0 akiﬁaM+uemw00kvwwm ,1 _ «I... N a. 0 N {.80. ..0_+. jinn 0:000 . . f. +Tgak+ﬁ0 __Em:_ . . . y E0- 30.- . AE- 0mag 003 .00530m Em;- ...
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