Hemchandracharya North Gujarat University 2002 B.Sc Computer Science 102 : Advance Mathematics - exam paper

(iii) If y = (sin x)x then obtain dy/dx 2






















3 (a) obtain : 6

x three + three x two +2
(i) ? ------------------------------ dx
X

__ __
(ii) ? ( v x + 1/v x )2 dx

2x-3
(iii) ? ------------------------ dx
x two - three x + two

(b) obtain the maximum and minimum values 3
of y = 2x3+ 9x two -24x + 6.
(c) obtain the points of inflexion of the curve 3
y = x four - six x three + 12x2 + 3x + 5.

OR
3 (a) obtain : 6

one
(i) ? ------------------------------ dx
9x2 + 4

(ii) ? x e x dx

(iii) ? e x ( sin x + cos x) dx.

















(b) The total revenue function is provided as three
R = 21x - x two and it’s total cost function
C = 1/3 x three - three x two - 7x + 16 where x is output.
obtain :
(i) The output at which the total revenue
is maximum.
(ii) The output at which the total cost is
minimum.
(c) obtain the interval in which curve 3
y = x four - six x three + 12x2 + 5x + 7. is concave

Earning:   Approval pending.