12.11.2003
1.00  4.00
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI– 600 034
B.A. DEGREE EXAMINATION  ECONOMICS
FIFTH SEMESTER  NOVEMBER 2003
EC 5404 MATHEMATICS FOR ECONOMICS
Max: 100 Marks
PART  A
Answer any FIVE each carries FOUR marks.
(5  4 = 20 Marks)
01.
02.
03.
04.
What is differential calculus?
Find out the derivative of a function y = x2 .
What is meant by partial differentiation? Give an illustration.
For the utility function of two commodities U = (x1  2)2 (x2 +1)3 . Find the
marginal utility of x1 and x2 at x1= 3, x2 = 4.
05. Define integral calculus.
1 

06. Solve   e x  3  dx .
x 

07. The marginal cost function of a firm in 10010x + 0.1x2 where x is the output.
Obtain the total cost function of the firm when the fixed cost in Rs.500.
PART  B
Answer any FOUR; each questions carries TEN marks.
(4  10 = 40 Marks)
08. Differentiate the function: x3 y + y 2x = 0.
09. Prove that the first order differentiation of the function ex is ex.
10. If f(n) = x3 5x2 + 7, find the second order derivative of f(x) and for that value of x
does f 1(x) vanish?
11. Examine the curve y = x3 for convexity.
20
12. If the demand law is x 
, find ed with respect to price at the point
p 1
where p =3.
1
13. Integrate :
.
x 2
14. Find the area bounded by the parabola x2 = 4by, the x  axis and the ordinate at x =3.
PART  C
Answer any TWO each carries TWENTY marks.
(2  20 = 40 Marks)
15. Find the maximum and minimum values of the following function y = x3 3x +1.
16. Evaluate I =  x 2 log x.dx.
17. Max U = 48 (x 5)2 3 (y 4)2
s.t x+3y = 9  x, y b 0.
18. Give the demand and supply functions pd 
8
1
 2 and Ps  ( x  3),
x 1
2
Find the price of the quantity demanded and the consumer surplus.
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