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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
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
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. Derivativ
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 arcco
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. Derivat
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
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 follow
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 s
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
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 rul
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. Defin
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 answ
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
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 margina
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 b
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 $5
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
2
1
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( x + 3)( x + 4 )
( x 2 )( x 6 )2
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e2 +1
2.
e +1
3.
1 + ln( x 1)
dx
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0
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y = x2 + x + 6
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 enclos
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 ti
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 =
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)?
Dierentia
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