EIA1007 Elementary Mathematics
2015/16 Sem 2
Tutorial 6
Differentiation (cont)
1.
Find the derivative of the function
a.
b.
c.
d.
e.
f.
2.
Find the second derivative of the function.
3.
Find the derivative of the function
a.
b.
c.
d.
e.
4.
Find the second
EIA1007
Elementary Mathematics
1.
Tutorial 11: Solution
Definite Integration
Using the fundamental theorem of calculus, find the area of the region under the graph of the
function on the interval [a, b].
a)
,
,
b)
c)
,
ANS: 16 sq unit
,
. ANS:
.
ANS:
d)
2
EIA1007 Elementary Mathematics 2015/16 Sem 2
Tutorial 4
Limits & Continuity
S.T. Tan (5th Edition) Chapter 9 Exercise 9.1 page 548
7, 11, 18, 38, 59, 66, 68, 86
7. The limit does not exist. If we consider any value of x to the right of x = -2, f (x) < 2.
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Financial
Economics
Topic 10
Valua1on of Bonds
Total Slides: 61
2
Introduc1on
A bond is a long-term debt instrument issued by
the borrower (government or corpora@on).
Government or corpora@on collects
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Financial
Economics
Topic 3
The Central Bank
Total Slides: 55
2
The Roles of Money
Money is anything that is generally accepted as a
medium of exchange.
What sellers generally accept and buyers ge
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Financial
Economics
Topic 9
Valua1on of Stocks
Total Slides: 51
2
Introduc1on
Stock valua5on aims to determine the intrinsic
value of a stock, i.e., how much a stock is worth.
The es5mated stock valu
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Financial
Economics
Topic 7
Ecient Markets Hypothesis
(EMH)
Total Slides: 54
2
Total Slides: 54
3
Total Slides: 54
4
Total Slides: 54
5
Which one is related to EMH?
Total Slides: 54
6
The Hi
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Financial
Economics
Topic 5
Time Value of Money
Total Slides: 48
2
Time Value
It is the process of expressing:
The present in the future
(compounding)
The future in the present
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Financial
Economics
Topic 12-13
Cost of Capital & Capital Budge9ng
Total Slides: 47
2
Introduc9on
The capital structure of a rm is the mix of dierent
securi;es issued by the rm to nance its
opera;on
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Financial
Economics
Topic 6
Risk
Total Slides: 49
2
Deni7on of Risk
Uncertainty: Risk means the uncertainty of future
outcomes.
For instance, the future value of an investment in
Googles stock i
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Financial
Economics
Topic 4
Securi3es Markets
Total Slides: 53
2
What is a Market?
It brings buyers and sellers together to aid in the
transfer of goods and services.
It does not need to have a p
EIA 1007
Elementary Mathematics
Tutorial 10
Integration
2015/16 Sem 1
1.
Find the indefinite integral.
2.
Find f(x) by solving the initial value problem.
3.
As part of a quality-control program, the chess sets manufactured by Jones Brothers are subjected
EIA1007
Elementary Mathematics
Tutorial 9
Calculus of Several Variables
1.
Let
Compute f(1, 2), f(2, - 1)
2.
Let
3.
Body mass index (BMI) is used to identify, evaluate, and treat overweight and obese
adults. The BMI value for an adult of weight (in kilogr
Mock Test 1
1. Find the slope of the line that passes through the given pair of points.
( 1, 2) and (3, 4)
a.
b.
c.
d.
2. Find the slope of the line that passes through the given pair of points.
(2, 2) and (8, 5)
a.
1
2
b. 2
c. 10
7
d. 7
8
e. 1
2
3. Find
Mock Test 2
1.
Determine whether the equation; 4x + 7y = 14 defines y as a linear function of x. If so, write it in the
form y = mx + b .
a.
b.
c.
d.
2. Determine whether the equation; 8x = 5y
y = mx + b .
a.
b.
c.
d.
8
5
8
=
5
9
5
9
5
=
=
=
9 defines y a
Mock Test 4
1. Use the graph of the given function f to determine
at the indicated value of a, if it exists.
a.
b.
c.
d. The limit does not exist
2.
Complete the table by computing
(if it exists).
a.
b.
at the given values of x. Use these results to estim
Mock Test 3
1. Evaluate the expression
a.
b.
c.
d.
10
729
9
6
2. Evaluate the expression.
a.
b.
c.
d.
27
24
2
3
3. Evaluate the expression.
a.
b.
c.
d.
e.
4. Evaluate the expression
a.
b.
c.
d.
- 64
- 25
- 125
- 124
5. Evaluate the expression.
a.
b.
c.
d.
EIA1007
Elementary Mathematics
Tutorial 8
Application of Derivatives - Solution
Sem 2 2015/16
Tan(2010), pg 739
27.
f(x) = 2x2 + 3x - 2; (, )
f '(x) = 4x + 3.
Setting f '(x) = 0 gives x = -3/4 as a critical point of f.
Next, f "(x) = 4 > 0 for all x, so f
Differentiation
MULTIPLE CHOICE
1. Find the derivative of the function by using the rules of differentiation.
a.
b.
c.
d.
2. Find the derivative of the function by using the rules of differentiation.
a.
b.
c.
d.
3. Find the derivative of the function f by