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

The Area Problem
Outline The Definite Integral
The second fundamental problem in calculus is to calculate area of the
region bounded by the graph of a nonnegative function f, the x-axis,
and the vertical lines x = a and x = b. This area is called the area

MATH 001 Calculus
House Rules
Groups:
G5: Monday 12:30 p.m to 3:15 p.m.
G6: Tuesday 8:15 a.m to 11:30 a.m.
Venue: SOE/SOSS SR3-3
To maximise your gain from this course:
Attend all lessons
The lessons build upon one another. Missing one would be difficul

Home Work Week 03: Limits, Continuity and Derivative
Q1:
Solve x (with the help of calculator) for
x
(a) 3 = 87
3
(b) x = 87
(c) x=log5267
(d) log(3x+2) + log(x+1) = 2log(x+4)
Q2. How many years will it take $5,000 to grow to $7,500 if it is invested at a

Graphing Strategies
Graphing Strategy Example 1
Step 1. Analyze (x).
(a) Find the domain of .
(b) Find intercepts. x intercepts and y intercepts
(c) Find asymptotes. vertical and horizontal asymptotes
Step 2. Analyze '(x)
Find the partition numbers for, a

Application: Approximation using
differentials
Lecture 5 Applications of Differentiation
Lecture 05
Applications of Differentiation
Approximation using differential
Marginal Analysis
(x+x, f(x+x)
f(x)
Slope of tangent = f(x)
y
(x,f(x)
First Derivativ

Home Work Week 06: Application of Differentiation and Optimisation
1. Point of diminishing returns:
A baseball cap company is planning to expand its workforce. It estimates that the number of
baseball caps produced by hiring x new workers is given by:
T(x

Home Work 09: Indefinite Integral, Differential Equation and Definite Integral
1. Find the Indefinite Integral of the followings:
1.
2.
3.
x (x 2) dx
2
3
x ( 2 X 1)
2
2
dx
ex
1 e x dx
1
x ln x dx
(ln x )3
5.
dx
x
4.
2. Application of Integration: The