Tiêu đề 1. Calculus DEC 2016 MAIN EXAM QP solved.pdf ✅

.l r -l ttlt t PARTA .,taswet ALL questions I rd' nr.mn.r,- - h- -r(r);,1-l ..n\.''.'..-r....r'- r:' RclNo, Name..... . ""' APJ ABDUL I(ILAM TECH]'{OLOCICAL UNIVERSITY TIRST SEMESTER B,TLCH DEGREE EXANIIN TION. DEC 20 I6 (1016 ADMISSION) Coursc Code: MA tUl CotrrseNrnd CALC!LUS Drmlnrn: I Ilours (b) l_ind (hc Maclaurin seies 6rthe ]nnc rn r€r (i) : 's, ll-r).rr1 r"J " _: r:\ (L) Coorp e rhe difitEnrhl .i, .ldrc inncrion z = tdn 1Or- (r) r (n) Iindrbcd.drinorr(r)=(Jst+1,t'z),.0=1,.,rr(,0) (rl (b) I ind the dnecrional dqivdivc ol f(x,y) = e'r ar P (5,0 ), iD tl& (r) ai'*ti.""r,=-li+ii I r-fx , r. J, l" =:;7. , (h) UsedoubLr inrcgornrnl. iind lhe deaolthe plDnetgi.n endos.d b], the (r) -{iven cuNes / = sina and y=.osr tbroconve€ence ot rhe series PART B (Each q"$tioh .anies I Mn,kg A swer aa! TyO qaestio,s ur L5e sms ,r=1 +=r: ,h( rre" Xf=1r-1)^+1L is ahsolurely !on\ergcnl or of convergence and interaat of Ans||zr dh! IWO qu.sriohs l. u - t() - /,? -r_\ ./) pro\- ri.r 31, ,r _9" _ 0 |uflD1lf, jl- r ry, .A\er I h a,oc" .Fe,r .op.oln,r.rn I, tl t )' 2 \ - 4\ - 5 ro /'1,.)'r' a poin, p. D.,.m.,lr rh. porn, t l^ r^.,:" * J\.rer1c o,rrr,unclol/r).),). r/_4r or R \r'er li a h\ lrdnf , tc. ret on wir'1.e. tr-!,0.r j,0 rr and Ld.O, Ansnet drr! TWO qu"rriohs Evatuate lhe deinrc inEsEt/ (erti + e-tj + 2\tE Ddt. li.d rhe vetocny. accetenrion. speed. scatar ransenrial abd nomat (o np.nenrs otJc!rteralron ar ih< pi,en rol .(r)=3snrr + 2costj _ sinzt k t=! lind rhc cquaron oflhe ransen, 0,,n" on, oo.i,"n," "ruo,,on ,0.,n" nohai lire to tire suface z = 4x3,2 + 2/ _ 2 ar the poinr (1.-2,10) 8 0 u I] I4 ti t6 t1 Ansttet ir! fWO questions Ev'rua,e the in,egrar fl lijTaray by tusteyebme rhe order or Ehraft !: r;, !;-, x ddxdy rind the volunrc otthe sotid tn the,irs ocrdr bounded hynrco_ordinare KTUQBANK.COM
plinesdndtheflancr+/+z = 1 ?ART C (Ench .!rcstio" .tnier i itotks) A"sr'd nr! THREE qu.stions r, Iind di! F andcurlF at F(a,y,z) = a'zyi + 2ytzj + 3zk 20 sho$ rhal v'7(.n) - n (n + 1)rn 'z \\neter = lli + yj +zk 2l Find the sol{ done br'fie lorcc licld F(,,y,z) = (.xz + xy) i + (y - x'zy)i on ! p: icr€ rhar norcs rrln rhr cu\( L't=.,,=-,Is.sJ 22 Evaluare JF.d, rvhcEF(a,1,)=/i ,j alon-{ rhc rianslejoi.ine the vedices (0.0). (1.0). and(0.1). 2l Dereftine wbether F(r,/l = ay i + axl s a consrlative veclor field. If so. find the potenli.ltunction and lhe potential .n.rey. Arnret t! TITREE laestiohs 24 Usins Giem\ rhmeh culuarc d. (ex + y'z) dx + Gt + xt) dy) wheFchtuboundaryol re regionbe$eeny = t2 andy = 2r. l L.d L"k n! u lJe .nrc.m. I I :' rir o drepresentdd by the vccrorvalued nm$ion rQ,t) = 2casoi + uj + 2sinvk ,1, S u < 3, O < v < n 26 using Divergen e rhmrcN qalurc It F.r ds Nherer(r,/,2) = (x - z) i + (y - x)j + (22 - y)t . d h rlre $trI]lc. ol ifu .tlindical solidbormdcd b] xz +Y2 = @z,z - 0,2 = l. 2? Deremnre lherher the vecror 6eld F(a,y,r)=4(r3-r)i+ a(y3 y)j + 4(23 z)/. is frue of sourcs and sinks lr ir is.dr. 28 Usins stokes fieorem eldlu,rc l. F.dr shetu F(x,Y,z) = x'zi + +xY3 j + Y'1xk, C is$erecranBlc: 0 < 1 < 1,0 < y < 3 inilr plane = ty KTUQBANK.COM
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