Lovely Professional University 2008 B.Tech Computer Science and Engineering CALCULUS-II -PAGE-1 - Question Paper

CALCULUS-II page-1

MTH502: CACIJLUS-II    A

TIME: 3 HOURS    MAX.MARKS: 100

This paper contains 6 questions oo 2 pages.

Answer ail the questions,

Question-!.

(I)    Arc the following vectors linearly dependent or linearly independent: (U/m-K3),(0,l,2)_f(-3,7,2).

(II)    Show that sum of the Eigen values of tlie matrix *^{s e<}l^{ua10 sum}

elements of the principal diagonal.

(III)    Find the Laplace transform of e~^2tsin4t (rV) Find the Laplace transform of

(V) Find the inverse Laplace transform of log j

(5x2=10Marks>-

QuetiOD2.

(I)    FuidP.lof0 + = x² + 2x + 4 ---'

(II)    Find C.F. of 0 - 6 g + 9y = 3e²* + logx

(III)    find value of /(Euler's coeffi.) for the functton/(jt) = VI - cosx, 0 <x <2n

(IV)    Find the value of a₀ and a_n for the function f(x) = x in the interval-/! < x < n

(V)    Find a Fourier series for the function f(t) = 1 - t² when-1 t 5 1

(5x2=1 OMarks)

Ouestlon-3.

(I)    Verify the Cayley-Hamilton theorem for the matrix A and find its inverse where

*6 3

(II)    Investigate for what values of a and b the simultaneous equations :

(1) 2x + 3y + 5z = 9 (2) 7x + 3y - 2z = 8 (3) 2x + 3y + az = b have (1) no solution (2) a unique solution (3) an infinite number of solutions

(2xlO-20Marks)

1

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Earning:   Approval pending.