- 2 - Calculate the unit tangent and unit normal vectors with components of the curve x 4cos t, y 4sin tand z = t. Find these vectors when t 2.

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Dwain Gregory
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1 PART A [BAHAGIAN A] - - (EQT 41) Queston 1 Soalan 1 (a) Calculate the unt tangent an unt nomal vectos wth components of the cuve 4 t, 4 tan = t. Fn these vectos when t. [Dbe fungs 3 f, 3. Ka unt tangent an unt nomal vekto engan komponenkomponen bag lengkung 4 t, 4t an t. Ca vekto tesebut apabla t.] (10 Maks / Makah) f, 3. Calculate the ecton along, whch,1. Net, compute the ecton u 3 (b) Gven a functon f, ncease most apl at the pont such that uf 1,1 6. [Nlakan sepanjang aah, ang f, betambah engan cepat paa ttk ka aah u supaa uf 1,1 6.],1. Seteusna, (10 Maks / Makah).3/-

2 Queston Soalan (EQT 41) Vef that the Dvegence Theoem s tue fo the vecto fel F 3 e j k, whee S s the suface of the sol boune b the clne 1 an the planes 0 an. [Tentusahkan bahawa Teoem Kecapahan aalah bena untuk mean vekto S aalah pemukaan kepaa pepejal ang batas oleh F e j k, ang 3 1 an satah-satah 0 an.] (0 Maks/Makah).4/-

3 Queston 3 Soalan (EQT 41) The table below shows the ata of the sellng cas fom compan YZ n the peo of 6 months n ea 01. [Jaual bawah menunjukkan ata jualan keeta a sakat YZ alam tempoh 6 bulan paa tahun 01.] Month, No. of Sellng, B ug the Least Squaes appomaton, [Dengan menggunakan penghampan Kuasa Dua Tekecl,] (a) fom a staght lne equaton [bna pesamaan gas luus] ( 6 Maks / Makah) (b) fom a secon oe polnomal equaton [bna pesamaan polnomal pengkat ua] ( 10 Maks / Makah) (c) fn the eo of these both appomatons [ca alat bag keua-ua penghampan tesebut] ( Maks / Makah) () state the best metho whch has least eo an gve concluson. [natakan kaeah mana ang mempuna alat tekecl an bekan kesmpulan] ( Maks / Makah) All calculatons must be n 3 ecmal places. [Semua pengaan mestlah alam 3 tempat pepuluhan.].5/-

4 Queston 4 Soalan (EQT 41) Solve the followng ntal value poblem fo the heat equaton ug fnte ffeence metho up to t Use step se t 0. 01an 0.. All the calculatons must be n 3 ecmal places. [Selesakan masalah nla awal untuk pesamaan haba mengunnakan kaeah bea tehngga sehngga t 0.0 Guna selang t an 0.. Semua pengaan mestlah alam 3 tempat pepuluhan.] u u, 0 1, t 0 t u 0, t u(1, t) 0, t 0,0 4 (1 ), 0. u t (0 Maks/Makah).6/-

5 PART B [BAHAGIAN B] (EQT 41) Queston 5 Soalan 5 Let S be the poton of the suface 5 that les on the planes 0 an 0. [Anakan S meupakan sebahagan apaa pemukaan 0 an = 0.] 5 ang beaa paa satah (a) Sketch the suface S. [Lakakan antau S. ] ( Maks/Makah) (b) Evaluate the suface ntegal of the vecto fel F j k as S. [Nlakan pengaman pemukaan untuk mean vekto F j k seluuh S.] (18 Maks/Makah).7/-

6 Queston 6 Soalan (EQT 41) Fn an appomate soluton to the ntal value poblem [Ca penelesaan penghampan bag masalah nla awal] 1 t 4 t, 0 1 n the nteval 0 t 0. ug the fouth oe Runge-Kutta metho wth h t Compute the eact value gven b t e. Net, compute the absolute eo an the pecentage elatve eo. All calculatons must be n 4 ecmal places. [alam selang 0 t 0. menggunakan kaeah Runge-Kutta pengkat empat engan h 0.1. Ka nla t sebena ang be t e. Seteusna, ka alat mutlak an peatus alat elatf. Semua pengaan mestlah alam 4 tempat pepuluhan.] (0 Maks / Makah) -ooooooo-

7 - 8 - ATTACHMENT / LAMPIRAN (EQT 41) Pola Coonate of Plane Suface Integals s S S F S F n S S Dvegence Theoem, Pola Coonate of Clne v F V. V F S ~ S ~ ~ Lnea Regesson v s S V S S S S a n S n S b n S S S S S Pola Coonate of Sphee S V Tgonomet Popetes Polnomal Regesson an b c 3 a b c a b c 3 4 Fnte Dffeence Metho u k k t, h, t 1 u, t u1, t u h, t u 1, t Fouth Oe Runge-Kutta Metho 1 4 k hf, h k1 k hf, h k k3 hf, k hf h, k 1 k k k k

SULIT (EQT 203) PART A [BAHAGIAN A] Question 1 Soalan 1

SULIT (EQT 203) PART A [BAHAGIAN A] Question 1 Soalan 1 PART A [BAHAGIAN A] Questio 1 oala 1 - - (EQT 03) olve the followig iitial value poblem fo the heat equatio ug fiite iffeece metho up to t 0. 0. Use step sie t 0. 01, 0. a thee (3) ecimal places i calculatio.