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Guru Gobind Singh Indraprastha Vishwavidyalaya 2008-2nd Year B.C.A Computer Application Mathematics-III, Third Semester, End Term , Year , , - Question Paper

Tuesday, 28 May 2013 12:45Web

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End Term Examination

TuiKOSiMun>lBC*]Dl< imim-HM

|PMr Com.-' BCAttf    Subfttt UMhWnMtCtlB '

|*yr    _______(Beh tt*S-2*0T) '

Ttmt 3 Mom    "    ____________Maxin*mMt*t:7t

i    __ MO* Of * couWary.

Q1 4) Prove that the argument of the product of three complex numbers is equal to the sum of their arguments IWFind V|r]*

r'


(cjfind PI for the differential oquabon <D' - iD + 2)y- 2*cJ.

(>4s it possible to nave Fourier expansion of the function given by f(x) = sin - in

(he interval (st.x).

(e) Prove friat ((- t)*J a not a Canchy Sequence is it bounded?

<fl Evaluate Mm

'/    n -(*[ 2 3 nJ

JffCWcuss the convergence of -Jn tui .

jpftf imwxr. then prove that w|cvf v, where w it a constant vector

ti) Write the Fourier expansion of 'Stete Root test snd Rato test for series Which of them is Mronger?(Z.5x1025)

Q2 (a) Sotve-JHf -    00 *2x-x,*xy = l

iit y-x-4    , dt at ta

mT + 2T + y = **<x*x*    (3*5*4.5) at

Oft

+\)y"sit\xsk\2x    vtcy (6+#.S) at l*x

03 (a) Find the Fourier series for the function given    by /($= xi'mx.-x < x <*.

___,    . T I I I

Deduce** rrrr-*...

axe. 0 S *

(b) If    /(<>-


(/-*). i<*</

/WsiAstoir- Akso. find the sum u-L.    (S*.S)

OR

(a>Find the half-range cosine series tor (x-1)2. 0<x<1 Deduce that y    \ I

6 2"*37

then


thow


that

that

(8*6.5)


Deduce


0 -*txi0

o /w-| 0<,<jr.


I i


(a)ProvetfialVx{Vx5)-v*a+V(V5).    (6)

(b)    Verify Green's theorem in the plane tor - *y! )fa * (4> - 6rv), where C

it the boundary of the region bounded by y = Jx and y *j1.    (6.8)

Oft

(a)pr0vematv,(/)=vav*2v*w*'jv4*.    ()

(b)Utw>o    Green* theorem, evaluate -(jt 1 ~2xy)dx+{x'y*l)dy around the boundary of the region grven by y*>8x and x=2.    (6.6)

t

(a)    Express s>n*8 in terms of cosnes of multipies of 9.    (9.6)

(b)    Show that the sequence <x> given by Xi*1, - 3*. nil is

2 *,

convergent to 41

(7)

()

U7)


OR

(a) If Z-co0+/ski0. then prove that Z"- =    -

(b) Test the convergence of the senea


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