PROGRAMME OF ECONOMICS
SCHOOL OF ECONOMICS, FINANCE AND BANKING (SEFB)
FIRST SEMESTER 2023/2024 SESSION (A231)
BEEQ2013
MATHEMATICAL ECONOMICS
GROUP C
ASSIGNMENT 3
COURSE LEARNING OUTCOMES
Upon completion of this course, students would be able to relate systematically and critically, the
effect to the economic models, as a result of changes to some environmental factors. (A4) (PLO2)
EVALUATION
This assignment is account of 20% of overall marks for BEEQ2013 as indicated in the syllabus and
will be evaluated based on Numeracy Skills Rubric (LOC3e).
INSTRUCTIONS TO STUDENTS
1.
This assignment will be completed as a group discussion and submit only ONE (1) set of
answers.
SUBMISSION GUIDELINES
1.
2.
You must submit this assignment via UUMOL (by leader only) before 5.00 pm on 25
January 2023 (Thursday).
Submitted after the date will NOT be accepted.
1
THE TASK
Topic 3
A. Find the partial derivative of the following functions:
1)
𝑧 = 𝑓(𝑥, 𝑦) = 𝑥 2 + 𝑦 2
2)
𝑧 = 𝑓(𝑥, 𝑦) = 𝑥 2 𝑦 3 − 10𝑥
3)
𝑧 = 𝑓(𝑥, 𝑦) = 3𝑥 2 𝑦 2
4)
𝑧 = 𝑓(𝑥, 𝑦) = 𝑥 6 𝑦 2 + 5𝑦 3
1
3
5)
6)
7)
8)
𝑧 = 𝑓(𝑥, 𝑦) = 16𝑥 4 𝑦 4
𝑧 = 𝑓(𝑥, 𝑦) = (3𝑥 + 5)(2𝑥 + 6𝑦)
𝑧 = 𝑓(𝑥, 𝑦) = 3𝑥 2 (5𝑥 + 7𝑦)
6𝑥+7𝑦
𝑧 = 𝑓(𝑥, 𝑦) = 5𝑥+3𝑦
9)
𝑧 = 𝑓(𝑥, 𝑦) =
10)
𝑧 = 𝑓(𝑥, 𝑦) = 𝑥 2 + 𝑦
11)
12)
13)
14)
15)
16)
𝑧 = 𝑓(𝑥, 𝑦) = (𝑥 + 𝑦)2
𝑧 = 𝑓(𝑥, 𝑦) = 𝑒 𝑥 𝑦
𝑧 = 𝑓(𝑥, 𝑦) = 3𝑥 3 − 2𝑒 𝑦
2
𝑧 = 𝑓(𝑥, 𝑦) = 𝑒 2𝑥 +3𝑦
𝑧 = 𝑓(𝑥, 𝑦) = 𝑙𝑛(7𝑥 + 2𝑦)
𝑧 = 𝑓(𝑥, 𝑦) = 𝑙𝑛(𝑥 2 + 4𝑦 2 )
𝑥+𝑦
3𝑦
𝑦
𝑥
B. Find the total differential of the following functions:
*Please use the same questions in (A).
C. Find the total derivative of the following functions:
1) 𝑧 = 𝑥 2 + 𝑦 2 where 𝑥 = 𝑡 and 𝑦 = 2𝑡
2) 𝑧 = 𝑥 2 𝑦 where 𝑦 = 7𝑥 2
𝑥+𝑦
3) 𝑧 = 3𝑦 where 𝑥 = 2𝑦 2
4)
5)
𝑧 = 𝑒 𝑥 𝑦 where 𝑥 = 𝑦 2
𝑧 = ln⁡(7𝑥 + 2𝑦) where 𝑥 = 𝑡 and 𝑦 = 4𝑡
D. Find the derivative of the following functions:
1) 𝑥𝑦 − 𝑦 3 + 𝑦 = 0
2) 𝑥 2 𝑦 + 4𝑥𝑦 2 = 6
3) 𝑦𝑒 𝑥𝑦 − 10 = 0
4)
5)
6)
𝑥 2 +𝑦 2
𝑥+𝑦
=5
ln(7𝑥 + 2𝑦) = 2
ln(𝑥 2 + 4𝑦 2 ) − 3 = 0
2
Topic 4
1.
2.
3
3.
Topic 5
1.
i)
ii)
iii)
iv)
2.
4
3.
5