advanced mathematics 1 jan 2014
TRANSCRIPT
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
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(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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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[---
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' .. .. '",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
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at (1, -1, 0)." A(x.Y-z),,,,':
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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$)
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Evaluate [ |. [.''' ''dxdydz. (06 Marks)
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t,Find the rurr. or l[f)r rrru rr,! vqru! vr
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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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(07 Marks)
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