Студопедия
Случайная страница | ТОМ-1 | ТОМ-2 | ТОМ-3
АрхитектураБиологияГеографияДругоеИностранные языки
ИнформатикаИсторияКультураЛитератураМатематика
МедицинаМеханикаОбразованиеОхрана трудаПедагогика
ПолитикаПравоПрограммированиеПсихологияРелигия
СоциологияСпортСтроительствоФизикаФилософия
ФинансыХимияЭкологияЭкономикаЭлектроника

Mathematics II

Читайте также:
  1. FROM THE HISTORY OF EARLY MATHEMATICS
  2. Lewis Carroll — Professor of Mathematics
  3. MATHEMATICS IN GREECE AND ROME
  4. Mathematics/ Actuarial Science personal statement
  5. Reasons for need of development of the Electronic textbook on the discrete mathematics
  6. SOME PROBLEM MATHEMATICS, PHYCICS, CHEMISTRY.

Mathematics II

Mock exam (April 5)

Time allowed: two hours.

Candidates should answer eight of the following ten questions: six from Section A (60 marks in total) and two from Section B (20 marks each).

Electronic calculators are not permited in the examination.

Marks will be deducted for insufficient explanation within your answers.

 

Section A.

Answer all SIX questions of this section (60 marks in total)

1. Determine the values of parameters and such that the following system of equations has a unique solution, and, using a matrix method, determine this solution when and have these values

 

2. Given that the function is homogeneous of degree 1, determine expressions for in terms of .

 

3. Solve the following differential equation

 

4. Find and classify the critical points of the function .

 

5. Determine the following integrals: ,

 

6. Solve the differential equation: .

 

SECTION B

Answer two questions from this section (20 marks each)

 

7. a) Expand in ascending power of x as far as the term in . State the range of values of x for which the series is valid.

 

b) Suppose that consumer demand depends upon the price-trend according to the formula . Suppose also that the quantity available is determined in a similar way, by the formula . Write down the condition for equilibrium and determine the equilibrium price path if and . Is the solution stable?

 

8. a)Find the inverse of the matrix

b) A house-buyer takes out a loan of amount with a bank. The bank’s interest rate is fixed at 4% per annum and payments of are made at the end of each year. Let be the amount of loan outstanding after t repayments of P have been made.

Explain why

By solving this difference equation, find .

Suppose that the loan is to be completely repaid after 25 payments. Find an expression for P in terms L.

 

9. a) A consumer’s ‘utility function’ for goods X and Y is where x and y denote the amounts of X and Y consumed. The consumer spends a total of 660 dollars on X and Y, and the prices of each (per unit) are, respectively, 4 and 8 dollars. Find the quantities of X and Y that the consumer buys to maximize the utility function..

 

b) Solve the following differential equation

 

10. a) A sequence of numbers is obtained as follows: and every other number in the sequence is obtained by multiplying the previous number by 2 and adding 3. Find a general expression, in as simple a form as possible, for .

b)Given the objective function and the constraint function: .

Form the Lagrangian function and find point(s) that satisfy the first-order condition.

Classify stationary points using the second-order sufficient condition.


Mathematics II

Mock exam (April 5)

Time allowed: two hours.

Candidates should answer eight of the following ten questions: six from Section A (60 marks in total) and two from Section B (20 marks each).

Electronic calculators are not permited in the examination.


Дата добавления: 2015-11-14; просмотров: 43 | Нарушение авторских прав


<== предыдущая страница | следующая страница ==>
One little brown bird| Marks will be deducted for insufficient explanation within your answers.

mybiblioteka.su - 2015-2024 год. (0.006 сек.)