MATH 105: PRACTICE PROBLEMS FOR CHAPTER 5: SPRING 2010
INSTRUCTOR: STEVEN MILLER ([email protected])
Question 1 : Dene the following terms:
(1) What does it mean for a function : 2 to be bounded?
(2) Dene a simple region.
Question 2 : Compute
4
2
=
=1
.
MATH 105: PRACTICE PROBLEMS FOR CHAPTER 1
AND CALCULUS REVIEW: SPRING 2010
INSTRUCTOR: STEVEN MILLER ([email protected])
Question 1 : These problems deal with equations of lines.
(1) Find the equation of the line going through the points (2,3) and (4,9).
Math 105 - Multivariable Calculus (Miller) -
Practice Midterms - 2010
First Practice Midterm
1. (20 points) Let (, ) = 3 + cos and (, ) = 42 + . Find the derivatives of the following
functions if possible; if it is not possible to nd the derivative state
MATH 105: PRACTICE PROBLEMS FOR CHAPTER 2: SPRING 2010
INSTRUCTOR: STEVEN MILLER ([email protected])
Question 1 : These problems deal with open sets.
(1)
(2)
(3)
(4)
(5)
(6)
Let
Let
Let
Let
Let
Let
= cfw_(, , ) : 32 + 4 2 + 5 2 < 6. Is open?
= cfw_(, ) :
MATH 105: PRACTICE PROBLEMS FOR CHAPTER 5: SPRING 2010
INSTRUCTOR: STEVEN MILLER ([email protected])
Question 1 : Dene the following terms:
(1) What does it mean for a function : 2 to be bounded?
(2) Dene a simple region.
Solution: (1) A function is bound
MATH 105: PRACTICE PROBLEMS FOR CHAPTER 3: SPRING 2010
INSTRUCTOR: STEVEN MILLER ([email protected])
Question 1 : Compute the partial derivatives of order 1 and order 2 for:
(1) (, , ) = + cos() sin().
Solution: We can proceed by brute force, but it helps
MATH 105: PRACTICE PROBLEMS FOR CHAPTER 6 AND
SEQUENCES AND SERIES: SPRING 2010
INSTRUCTOR: STEVEN MILLER ([email protected])
Question 1 : State the change of variable theorem in the plane. How does the element
transform in polar coordinates? How does tr
MATH 105: PRACTICE PROBLEMS FOR CHAPTER 3: SPRING 2010
INSTRUCTOR: STEVEN MILLER ([email protected])
Question 1 : Compute the partial derivatives of order 1 and order 2 for:
(1) (, , ) = + cos() sin().
(2) (, ) = sin( / ).
Question 2 : Compute the second
MATH 105: PRACTICE PROBLEMS AND SOLUTIONS
FOR CHAPTER 2: SPRING 2010
INSTRUCTOR: STEVEN MILLER ([email protected])
Question 1: These problems deal with open sets.
(1) Let = {(, , ) : 32 + 4 2 + 5 2 < 6}. Is open?
Solution: Yes: This is an ellipsoid where
MATH 105: PRACTICE PROBLEMS FOR CHAPTER 6 AND
SEQUENCES AND SERIES: SPRING 2010
INSTRUCTOR: STEVEN MILLER ([email protected])
Question 1 : State the change of variable theorem in the plane. How does the element
transform in polar coordinates? How does tr
MATH 105: PRACTICE PROBLEMS FOR CHAPTER 1
AND CALCULUS REVIEW: SPRING 2010
SOLUTION KEY (PLEASE REPORT ANY ERRORS TO ME)
INSTRUCTOR: STEVEN MILLER ([email protected])
Question 1 : These problems deal with equations of lines.
(1) Find the equation of the l