Homework Assignment #4
Calculus 1
Semester I, 2012
Due date: Wednesday, October 17, 2012 at the beginning of class.
1. For the function g whose graph is given, state the value of each quantity, if it exists. If it
does not exist, explain why.
(a) lim R (x
Homework Assignment #5
Calculus 1
Semester I, 2012
1. Prove that
sin x
tan x
ex 1
ln (x + 1)
(a) lim
= 1, (b) lim
= 1, (c) lim
= 1, (d) lim
= 1.
x0 x
x0
x0
x0
x
x
x
Hint: Using the definition of derivative.
Solution
(a) See the lecture note (slide 44).
(b
Calculus 1
HW Assignment #7
November 2012
Due on Wednesday, November 28, 2012 at the beginning of class
1. A ball is thrown vertically upward with a initial velocity 80 ft/s (feet/second), then its height
after t seconds is
s = 80t 16t2 .
(a) At what time
Homework Assignment #3
Calculus 1
Semester I, 2012-13
HW#3 will not be collected or graded.
1. For the function g whose graph is given, state the value of each quantity, if it exists. If it
does not exist, explain why.
(a) lim g(t),
(b) lim+ g(t),
(c) lim
HW Assignment #8
Calculus 1
December 2012
This homework assignment will not be collected or graded.
1. Using the lHospitals rule to find the limits
2x
x)
sin 4x
, (c) lim tan
,
(a) lim e x31 , (b) lim ln(ln
x
5x
x0
x
x0
ex 1x 12 x2
.
x3
x0
(d) lim
2. For
HW Assignment #9
Calculus 1
December 2012
Due on Wednesday, December 19, 2012 at the beginning of class
1. Evaluate the integral formula
R
R
R
R
2
a. x sin xdx, b. (2x + 9) ex dx,
c. x3 ln xdx, d. (lnxx)
dx.
2
(Hint for a c: Use the Integration by Parts.
Calculus 1
HW Assignment #7
Fall, 2012-13
8. (b) Use the Mean Value Theorem to prove the inequality |sin a sin b| 6 |a b| for all a
and b.
Hint:
For any value of a and b (suppose that a < b), by applying MVT, there exists a value of c in
(a,b) such that:
Example 9.1 Consider the case of a security whose price is $100, while
the risk-free interest rate is 4% per annum, the annual volatility of the stock
price is 23%, the strike price is set at $105, and the expiry date is 3 months.
Under these conditions t
Solutions Manual to
AN INTRODUCTION TO MATHEMATICAL
FINANCE: OPTIONS AND OTHER TOPICS
Sheldon M. Ross
1
1.1 (a) 1 p0 p1 p2 p3 = 0.05 (b) p0 + p1 + p2 = 0.80
1.2 P cfw_C R = P cfw_C + P cfw_R P cfw_C R = 0.4 + 0.3 0.2 = 0.5
1.3 (a)
8 7
14 13
=
56
182
(b)
6
Exam
Name_
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
1)
Activity in money markets increased significantly in the late 1970s and early 1980s because of
A)
rising short-term interest rates.
B)
reg
242Frederic S. MishkinEconomics of Money, Banking, and Financial Markets, Seventh Edition
Chapter 15
Multiple Deposit Creation and the Money Supply Process
)1
Multiple Choice
()a
()b
()c
()d
()e
()f
The government agency that oversees the banking system a
Chapter 14Structure of Central Banks and the Federal Reserve System 211
Chapter 14
Structure of Central Banks and the Federal Reserve System
)1
Multiple Choice
()a
()b
()c
()d
()e
Americans fear of centralized power and their distrust of moneyed interests
Chapter 11Economic Analysis of Banking Regulation131
Chapter 11
Economic Analysis of Banking Regulation
)1
Multiple Choice
()a
Although the FDIC was created to prevent bank failures, its existence encourages banks to
()b take too much risk.
()c hold too m
Chapter 12Nonbank Finance161
Chapter 12
Nonbank Finance
)1
Multiple Choice
()a
The federal regulatory agency responsible for regulating the activities of life insurance
companies is
()b the FDIC.
()c the Fed.
()d the FHLBS.
()e none of the above; there is
Chapter 8An Economic Analysis of Financial Structure9
Chapter 8
An Economic Analysis of Financial Structure
)1
Multiple Choice
()a
()b
()c
()d
()e
American businesses get their external funds primarily from
bank loans.
bonds and commercial paper issues.
s
Chapter 7The Stock Market, the Theory of Rational Expectations, and the Efficient Markets Hypothesis 237
Chapter 7
The Stock Market, the Theory of Rational Expectations,
and the Efficient Markets Hypothesis
)1
Multiple Choice
()a
()b
()c
()d
()e
()f
Stock
Chapter 6The Risk and Term Structure of Interest Rates197
Chapter 6
The Risk and Term Structure of Interest Rates
)1
Multiple Choice
()a
()b
()c
()d
()e
The risk structure of interest rates is
the structure of how interest rates move over time.
the relati
26Frederic S. MishkinEconomics of Money, Banking, and Financial Markets, Seventh Edition
Chapter 2
An Overview of the Financial System
)1
Multiple Choice
()a
()b
()c
()d
()e
Every financial market has the following characteristic:
It determines the level
130Frederic S. MishkinEconomics of Money, Banking, and Financial Markets, Seventh Edition
Chapter 5
The Behavior of Interest Rates
)1
Multiple Choice
()a
()b
()c
()d
()e
If wealth increases, the demand for stocks _ and that of long-term bonds _.
increases