Hemchandracharya North Gujarat University 2006 B.Sc Computer Science 102 : Advance Mathematics - Question Paper

one z xy


0 four three
(ii) If A = one -3 -3 then prove that A2 = I .
-1 four four


OR

2 (a) If A={x | x ? N, x3-2 = 25} , B={y y ? N, one < y <5} , 4
C={z z ? N, z4 = 81} then verify the An(BnC) U (AnC) .

(b) Answer the subsequent : 4

(i) If f(x)= x(x+1) (2x+1) then prove that f(x)-f(x-1)=6x2 .

(ii) obtain adjoint of the metrix , A= two -5 .
seven nine

(c) Answer the subsequent : 4

(i) obtain lim x -2 + 3x -3
x->8 5x -2 + 7x -4

(ii) obtain lim v x2 + 5x – x .
x->8

3 (a) If y = log ( 3x+4 ) e 2x+3 obtain dy . 4
dx

(b) Find dy
dx

(i) xy = yx

(ii) y = xex

one -1 one one then prove that 4
(c) If A= two -1 , B= four -1

(A + B)2 = A2 + B2 .


OR

3 (a) obtain lim ( x+2 )3/2 – ( a+2 )3/2 4
x->1 x – a

(b) obtain the subsequent : four

Earning:   Approval pending.