S277-S280_Krugman2e_PS_Ch20A.qxp
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chapter:
Appendix: Indifference Curve Analysis of Labor Supply
1.
Leandro has 16 hours per day that he can allocate to work or leisure. His job pays a wage rate of $20. Leandro decides to consume
Calculus, Semester 2 Final, Sample variant
#1 One question from Theory for Semester 2 Final file
#2 The company sells its produce at two different markets with the demand
functions q 16 0.25p and q 13 0.15p . The fixed expenses are 20 and each
unit quanti
Calculus 1 MidTerm Theoretical Questions
A general definition must be given with specific examples for each
case that the definition covers.
1. The properties of logarithms and exponents.
2. Derivative of function of single variable and its geometric
mean
Sample MidTerm Exam, Calculus 1
#1 Find third derivative of
#2 Find derivative
ds
dt
of
sin( / 2 2 x )
s ln t
3 t
at x / 4 .
and write out tangent line equation at
t 1 .
# 3 Find derivative
y x arccos x
2
arcsin x
at x 1 / 2 .
x 1
#4 Find extremums of y
Calculus 1 FinalExam Theoretical Questions
A general definition must be given with specific examples for each
case that the definition covers.
1. The properties of logarithms and exponents.
2. Derivative of function of single variable and its geometric
me
Calculus, Semester 1 Final Exam, Sample variant
1
2
#1 Find partial derivatives of the function for s = ctg (t 2 / u ) at t = , u = 1 .
1
2
#2 For f ( x, y , z ) = xy + y z + x 7 z find tangent plane at x = , y = 1, z = 2 .
#3 Find the gradient of implici
MATH 211 Skills Review: Quadratic functions and thier graphs
A quadratic function is one of the form f (x) = ax2 + bx + c, where a = 0. You should be able (easily and quickly!) to do
any of the following:
Solve a quadratic equation ax2 + bx + c = 0 for x
MATH 211 Skills Review: Graphs of power functions and absolute value; transformations
Powers of x:
1. You should know the graphs of the equations
y = x2 , y = x4 y = x6 , y = x8 , etc.,
how they are similar and how they change shape as you increase the ex
Math 233
Real Optimization
version 9-28-05
No More Square Boxes!: You are trying to design an open ended rectangular box
that must have a volume of 48 ft3. The two long sides will be constructed from thin
sheets of aluminum and will cost $1 per ft 2 of ar
List of Theoretical questions for Semester 2 Final - 2010
Important: If you give a general definition, you must give specific examples
for each case that the definition covers.
1. List the general rules to find indefinite integrals. How do they change for
Calculus, Semester 2 MidTerm, Sample variant
#1 Find antiderivative
tg 7 x
cos 2 x dx .
5
#1(alternative) Find antiderivative like ex 17-28 on page 408.
#2 Find antiderivative
ln x
3
x4
dx .
#2(alternative) Find antiderivative
3
sin x
dx .
2 cos x 1
#4 On
List of Theoretical questions for Semester 2 Midterm
Important: If you give a general definition, you must give specific examples
for each case that the definition covers.
1.
2.
3.
4.
5.
Part 1. Definite and Indefinite Integrals
List the general rules to
S185-S196_Krugman2e_PS_Ch13.qxp
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chapter:
13
Perfect Competition and the Supply Curve
1.
For each of the following, is the business a price-taking producer? Explain your answers. a. A cappuccino caf in a university town where the
S171-S184_Krugman2e_PS_Ch12.qxp
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chapter:
12
Behind the Supply Curve: Inputs and Costs
1.
Changes in the prices of key commodities can have a significant impact on a companys bottom line. According to a September 27, 2007, articl
S141-S156_Krugman2e_PS_Ch10.qxp
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chapter:
10
The Rational Consumer
1.
For each of the following situations, decide whether Al has increasing, constant, or diminishing marginal utility. a. The more economics classes Al takes, the
S87-S100_Krugman2e_PS_Ch06.qxp
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chapter:
Elasticity
1.
Nile.com, the online bookseller, wants to increase its total revenue. One strategy is to offer a 10% discount on every book it sells. Nile.com knows that its customers can be
S127-S140_Krugman2e_PS_Ch09.qxp
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chapter:
Making Decisions
1.
Hiro owns and operates a small business that provides economic consulting services. During the year he spends $55,000 on travel to clients and other expenses, and the
Dr. Zs Math151 Handout #4.7 [Optimization Problems] By Doron Zeilberger Problem Type 4.7.1 : A farmer wants to fence an area of A square units and then divide it into n + 1 parts by placing n parallel fences parallel to one of the sides of the rectangle.
2
1
1.
)
)
( x + 3)( x + 4 )
( x 2 )( x 6 )2
(
)
) cos(3 x) 6 x 2 + x + 3 dx
dx
1
dx
2sin x + sin 2 x
x 1
dx
2x 1
)
e2 +1
2.
e +1
3.
1 + ln( x 1)
dx
x 1
: e x sin x dx
0
4. , :
y = x2 + x + 6
y = 6 3x .
5. ,
Ox , : y = x 1 , y = x + 1 .
(
6. 12
OPTIMIZATION PROBLEMS
1. A wire of length 12 inches can be bent into a circle, a square, or cut to make both a circle and a
square. How much wire should be used for the circle if the total area enclosed by the figure(s) is
to be a minimum? A maximum?
x
2.
Math 141 Calculus 1
Fall 2007
Optimization Handout
1. Josh the Farmer acquires some goats, and the goats and the sheep do not get along. He
wants to fence in a rectangular area of his eld, but this time he wants to divide it in half
with another piece of
Math 229 Practice Dierentiate
x
2. y =
1+ x
4. y = x sin x
3
1. y = x + 2
x
1
3. y = x +
3
x
2
5.
y = (x 1)7 (3x + 2)9
7.
y = 3x
9.
xy = 9
11.
y=
1
2x2
4
1
x2 y 2 = x + y
29.
y = x2 sin x2
1
12. y = 4
(x + 4x2 )3
3x 7
14. y =
x2 + 1
16. y = (x2 + 1)3 7
Mathematics Learning Centre
The rules of calculus
Christopher Thomas
c 1997
University of Sydney
Mathematics Learning Centre, University of Sydney
1
1
How do we nd derivatives (in practice)?
Dierential calculus is a procedure for nding the exact derivativ
Definite Integral
Group 1
1
2
1. Compute the integral xe x dx . The answer is 1 .
e
0
2
2. Compute the integral cos5 x sin 2 xdx . The answer is
0
2
.
7
4
3. Compute the integral tg 3 xdx . The answer is
0
4. Find improper integral
5. Find improper integr