Homework Week 04: Rules of Differentiation
Q1: Find the first derivative for the following
a) y = 2x / (1 + lnx)
b) y = (x2 4)/(x2 + 5)
c) y = [ln(x2 + 3) ]3/2
d) y = ln(x2 + 3)3/2
e) y = 4xe3x
f)
y = x4 ln(1+ x4)
g) = 812
2
h) = log 5cfw_5
i) = 10
2 1
Home Work Week 03: Exponential & Log Function, Limits, Continuity and Derivative
Q1:
Average Cost
A company manufacturing surfboards has fixed costs of $300 per day and total costs of $5100 per day at
a daily output of 20 boards.
(A) Assuming that the tot
Homework Week 02: Quadratic and Rational Functions
Q1: Profit-loss analysis.
A company that makes and sell memory chips establishes the followings :
Revenue function,
R(x) = x (75 3x)
Cost function,
C(x) = 125 + 16x
Where x is in millions of chips, and R(
MATH001 Homework Week01
Note: Please submit handwritten, non-typed, answers. There is no need to copying the
questions. Please state your name, matric number and class on the submission.
Q1: Solving the following inequalities:
(A)
x + 3 > 1 and x 2 < 1
(B
Homework Week 05: Application of Differentiations 1
1.
Pollution. A small lake in a resort area became contaminated with harmful bacteria
because of excessive septic tank seepage. After treating the lake with a bactericide,
the Department of Public Health
Homework Week 12 Several Variables and Partial Derivative
Q1.
, Find the first derivative fx and fy.
Q2.
Let f(x,y)=z= (3x + 2y)5
, find fx and fy.
Q3.
Q4. Find the second partial derivatives for:
Part 2: Optimisation
Q5 .
Find the critical points of the
Homework Week 05: Application of Differentiations 1
1.
Pollution. A small lake in a resort area became contaminated with harmful bacteria
because of excessive septic tank seepage. After treating the lake with a bactericide,
the Department of Public Health
Homework Week 04: Rules of Differentiation
Q1: Find the first derivative for the following
a) y = 2x / (1 + lnx)
b) y = (x2 4)/(x2 + 5)
c) y = [ln(x2 + 3) ]3/2
d) y = ln(x2 + 3)3/2
e) y = 4xe
f)
3x
y = x4 ln(1+ x4)
(Hint: For (g) to (i), d not use formula
Good Understanding
G.U.
Must Know
M.K.
Part I: Pre-calculus
Readings: Textbook
Appendix A
Ch.1-1 to Ch.1-2
Ch.2-1 to Ch.2-5
1
G.U.
1.1 Functions and their graphs
M.K.
1.2 Solving equations and inequalities
M.K.
1.3 Applications
2
1.1 Functions and thei
Quadratic Functions
If a, b and c are real numbers with a 0, then the function
f(x) = ax2 + bx +c is a quadratic function and its graph is a
parabola.
The general forms of quadratic functions:
y = ax2 + bx + c a0
(standard form)
y = a(x-h)2 + k a0
(vertex
MATH001 Homework Week01
Note: Please submit handwritten, non-typed, answers. There is no need to copying the
questions. Please state your name, matric number and class on the submission.
Q1: Solving the following inequalities:
(A)
x + 3 > 1 and x 2 < 1
(B
Homework Week 02: Quadratic, Rational and Exponential Functions
Q1: Profit-loss analysis.
A company that makes and sell memory chips establishes the followings :
Revenue function,
R(x) = x (75 3x)
Cost function,
C(x) = 125 + 16x
Where x is in millions of
Lecture 6 Optimisation & Graphing Techniques
Lecture 06
Applications of Differentiation
Optimisation
L Hopitals Rule
Graphing
Implicit Function
Related Rate
Elasticity of Demands
Optimisation: Example 1 Area and
Perimeter
The techniques used to so
Compound Interest
Compound Interest
Example 4: You deposit $1,000 in a bank at 5%. Calculate the amount
after 5 and 20 years, with simple interest, compound daily, yearly and
continuously.
Let
P = Principal,
r = annual interest rate,
t = time in years,
m
Home Work 10: Definite Integral and Application of Integration
1. Definite Integral: Evaluate the integral:
-1
1.
2.
-2
7
6
x
dx
x 1
ln(t - 5)
dt
t -5
2
2. Application of Definite Integral:
A company manufactures mountain bikes. The research department pr
Homework Week 05: Application of Differentiations 1
1.
Pollution. A small lake in a resort area became contaminated with harmful bacteria
because of excessive septic tank seepage. After treating the lake with a bactericide,
the Department of Public Health
Homework Week 11 Several Variables and Partial Derivative
Part 1 Integration by Parts
Evaluate the following:
Some may require use of the integration by parts formula along with techniques which we
have learnt earlier. Other may require the repeated use o
Revision
Revision
Exam Notes
Exam Matters the following are excluded:
Completing Square to find max/min for quadratic functions
4 Step process to find derivative
Riemann Sum for Integration
Application of Integration: Gini Index/Probability
Graph shi