LOYOLA COLLEGE (AUTONOMOUS), CHENNAI– 600 034

B.A. DEGREE EXAMINATION  –     ECONOMICS

FIFth SEMESTER  – NOVEMBER 2003

EC 5404  MATHEMATICS  FOR  ECONOMICS

12.11.2003                                                                                        Max: 100 Marks

1.00 – 4.00

 

PART – A                                                    (5 ´ 4 = 20 Marks)

Answer any FIVE each carries FOUR marks.

 

1. What is differential calculus?
2. Find out the derivative of a function y = x² .
3. What is meant by partial differentiation? Give an illustration.
4. 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.

5. Define integral calculus.
6. Solve .
7. 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                                                  (4 ´ 10 = 40 Marks)

Answer any FOUR; each questions carries TEN marks.

 

8. Differentiate the function:  x³ y + y -2x = 0.
9. Prove that the first order differentiation of the function e^x is e^x.
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.
12. If the demand law is    , find ed with respect to price at the point

where p =3.

13. Integrate :   .
14. Find the area bounded by the parabola x² = 4by, the x – axis and the ordinate at x =3.

 

PART – C                                                  (2 ´ 20 = 40 Marks)

Answer any TWO each carries TWENTY marks.

 

15. Find the maximum and minimum values of the following function y = x³ -3x +1.
16. Evaluate I = log x.dx.
17. Max U = 48 -(x -5)² -3 (y -4)²

s.t x+3y = 9   ”  x, y b³ 0.

18. Give the demand and supply functions and

Find the price of the quantity demanded and the consumer surplus.

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