Math 20300 Spring 2006 Final Exam Answers:
1a) 4( x ! 1) " 7( y ! 1) " 5 z # 0
b)
x !1 y !1 z
#
#
4
7
5
2a) 3 x 2 y , x 3 " 2 ye z ,
b)
3
7
y 2e z
90
2
c)
c) 3( x ! 1) " 3( y ! 1) " z # 0
3a) Absolutely convergent use the limit comparison test with
1
$n
3
1
MATH 203 Final Exam
December 18, 2008
Instructions: Complete every question in Part I (Questions 1-7.) Complete three of
the ve questions in Part II (Questions 8-12). Each question is worth 10 points.
No calculators or other electronic devices may be us
Department of Mathematics
Math 203
The City College of New York
Final Exam
Fall 2006
No calculators permitted. Answers may be left in terms of radicals, , e, etc and do not
need to be simplied unless stated otherwise. Each question is worth 10 points.
Par
Math 202
Part I
Final Exam
Spring,2008
Do all parts of the following six problems.
(1) Compute the derivative
dy
dx
for each of the following (18 points) :
y = 2arctan(3x) ;
(a)
Ans:
y=
3 ln(2)2arctan(3x)
.
(1 + 9x2 )
(b) y = x2 + xx ;
Ans: y = 2x + xx (l
Course Syllabus
MATHEMATICS 185
Spring 2008
Texts: 1) Billstein, Libeskind, Lott: A Problem Solving Approach to Mathematics for
Elementary School Teachers (Addison-Wesley Publ.) 9th ed.
2) STUDENT HANDOPUT PACKET available from the instructor.
Prerequisit