- Find the differential dy,given(10 marks, 5marks each):
(a)y=-x(2x2+3)
(b)y=(X-8)(7x+8)
2.Given S1={1,2,3},S2={a,b},and S3={m,n},find the Cartesian products: (21 marks, 7 marks each)
(a) S1XS2 (b)S2XS3 (c)S3XS1
3.Find the value of the following factorial expressions: (25 marks, 5marks each)
(a) 5!
(b) 6!
(c) 4!/3!
(d) 6!/4!
(e) (n+2)!/n!
4.Find the stationary values of the following functions: (10marks, 5arks each)
(a) Y=x4
(b) Y=-x3
Determine by the Nth-derivative test whether they represent relative maxima, relative minima, or inflection points
5.Let the demand and supply functions be as follows: (20 marks, 10marks each)
(a) Qd=51-3P (b) Qd=30-2P
Qs=6P-13 Qs=-5+5P
Find Pand Q by elimination of variables.(Use fractions rather than decimals.)
6.Find the characteristic vectors of the matrix (4 2) (14 marks)
( 2 1)
Sample Solution