USN

Advanced Mathematics - I

Time: 3 hrs.

,:.,i , Note: Answer any FIVEfull questions.

1 ' ;. Express the complex number (1 + i)(1 + 3i)

in the form x + iy.1+ 5i

MATDIP3Ol

(07 Marks)

(07 Marks)

(06 Marks)

(07 Marks)

(07 Marks)

(07 Marks)

(07 Marks)

Third Semester B.E. Degree Examination, Dec.2013 /Jan.20l4

Max. Marks:100

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c.

2a.b.

c.

a.

b.

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4a.

b.

c.

5a.

b.

c.

6a.

b.

c.

r ----.-,:---r- -. (3- J 'Find the modulus and amplitude of trExpand coso 0 in a series of cosines multiples of 0.

Find the nth deiivative of sin(ax + b).

If y: (sin-l x)2, Showthat (1-x')y,*, -(2n+l)xy,*, -n'.yn=fl

^[ r -3t2 IFindthenthderivativeof I +,. i'- l.[51x-ll (?-tf2x+3)J

Using Taylor's theorem, express the polynomial 2xr +7x2 +x - 6 in powers of (x - 1).(06 Marks)

Using Maclaurin's series. expand tan x upto the term containing "t.r'6 Y (07 Marks)usmg .vtaclaurrn's senes, expand ran x upto rhe term contammg x;,3\g;:{gN(0, Marks)

lf z =r' + y'' - 3axy then prove ,1'ru, 9'l = :t: ''^y \c)\

ovox axav iY

"Er.r{E&t \Sqi

Marks)- "-"- AyAx AxAy ,,il cetur*:: lEt r9\ 1 l6ElAF' J '

e x' + y3 + 3xy = I . find l|. '3[---

{,fr*Marks)\,frrgpp_-_

' .. .. '",CI2 0z iZ- 0zIf z: (x, y) and x=eo +e-u andy=e-'-e', provethat:--=* ;-Vfi.t0l Marks)

.) ^) D(u.v.w)If u = x+3y2 -23, y = 4x2yz, w = 222 -xy, find the value of

-

at (1, -1, 0)." A(x.Y-z),,,,':

',... ' (07 Marks)

Obtain ihe reduction formula for f sin" x dx . : (06 Marks)

A 1r- ? xdxE'v'aluate l----. (07 Marks)J lt )

i.!." -"Evaluate I If ., + eY )dydx (07 Mark$)

l3

lll

Evaluate [ |. [.''' ''dxdydz. (06 Marks)

J J J_000

t,Find the rurr. or l[f)r rrru rr,! vqru! vr

l(rL_

Prove that B(m,n) = g)]q.l(m + n)For More Question Papers Visit - www.pediawikiblog.com

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7 a. Solve 9 -.'*-" +x' .e-" .

dx

b. Solve 4,Y =*' -y' which is homogeneous in x and y..'tr dx xy4a:^, dv V ,.:,,,.{., r c. Solve * -

,. ., = e'* (x + 1) .

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s ,s_.

$o*d* {< {< * * {' ..t' ' : / \t{u{\

(06 Marks)

.,.m,(07{arks)

-.%,*"

,,,':1''"r" (o6 Marks)

MATDIP3Ol

(07 Marks)

(07 Marks)

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j'hn ,*

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==il;..=

..'1 '::: :a S

.=' * &d' lud

.:::''"':"

i ":1J' .' nl'S,::":l

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2 of2For More Question Papers Visit - www.pediawikiblog.com

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