Things to Remember for MTH 2003, 2205, and 2207
(Last Updated 04/27/2009)
Limit Definition of the
Derivative
lim
x 0
OR
lim
h 0
f ( x x) f ( x)
x
f ( x h) f ( x )
h
Example
f ( x) x 2 7 x 6
f ( x h) f ( x )
h
( x h) 2 7( x h ) 6 x 2 7 x 6
lim
h 0
h
x 2 2
BARUCH COLLEGE
MATH 2205
FALL 2007
MANUAL FOR THE UNIFORM FINAL EXAMINATION
Joseph Collison, Warren Gordon, Walter Wang, April Allen Materowski, Sarah
Harney
The final examination for Math 2205 will consist of two parts.
Part I:
Part II:
This part will co
Math 2207
Additional problems for the Final Exam Manual
A calculator is NOT permitted on this part
Y
a
X
b
1. The graph of f is shown in the figure above. Which of the following could be the
graph of the derivative of f?
Y
Y
a
b
b
a
X
a)
X
b)
Y
Y
b
a
X
a
Properties of Exponents and Logarithms
Exponents
Let a and b be real numbers and m and n be integers. Then the following properties of
exponents hold, provided that all of the expressions appearing in a particular equation are
dened.
1. am an = am+n
2. (a