MAC 2233
Exam1-Sample Exercises(SE)/Review
SE0. Try the following easy problems:
a. Find the distance between the points (-3, -1) and (5, -2).
b. Find the midpoint of the line segment joining the points (-5, 4) and (-3, -8).
f ( x)  2 x 2  6 x  5 , calculate f (1) .
2x  1
d. Given g ( x ) 
, find g ( a  1) and simplify.
1 x
c. Given
e. Given the following graph of f ( x ) 
( x 2  4) , determine the open interval(s)
in which the function is increasing or decreasing.
SE1. (a) In the state of Florida the sales tax T on the amount of taxable goods is 6% of the value of the goods
purchased (x), where both T and x are measured in dollars.
(i) Express T as a function of x.
and (ii) Find T(400)
and T(80.5).
f ( x)  2  3x  2 x 2 and g ( x)  2 x  1, find the following :
f (2  h)  f (2)
f (2  h)  f (2)
(a) f  g (2) (b)
and lim
h
h
h0
SE2. If
SE3.Find the following limits:
x 2  7 x  10
1 h 1
(ii ) lim
2
h
x 5 x  11x  30
h0
2
2
x 4
x  6x  8
(iii ) lim
(iv ) lim
x2
x 2  16
x2
x  4
(vi). F ( x)  x  3
for  2  x  0
 1  2x
for
0x2
(i) lim
Find
(v) lim
x 
3x  2
x5
lim F ( x)
x 0
SE 4. f ( x)  2 x  1 when  2  x  0
x
2
 6 x
find
lim
x 0
SE5.
when
0 x2
when
2 x4
f ( x)
Find f ( 2), f (0), f ( 1), and f ( 0.5).
and
lim
x2
USING RULES OF DIFFERENTIATION , find f ( x) if
f ( x)
MAC 2233 - M. RAHMAN
f ( x) 
1
x
f ( x)  33 x  2 x
Page 2
f ( x)  x 4  50 x 2  20 x  496
f ( x) 
7 x 2  8 x  10
5
SE6. USING RULES DO THE FOLLOWING:
a.) If G ( x)  (3 x 2  8 x  5)(81  20 x  10 x 3 ), then find G ( x) without multiplyin g the factors.
Do not simplify your answer.
b.) Find G (2) and simplify your answer for this.
x2  4
, find F ( x) and simplify your answer.
x2
x  2 x 2  3x 3
d .) f ( x) 
x2
c.) F ( x) 
SE7. Applications problems: Section 2.2 # 64(Profit from sale of pagers);Section 2.3 # 18, 40, 74, 76; Section 3.1 #
58; Section, 3.2 # 55
Read examples from each covered sections, assigned home work problems, quizzes, and class note!!!!
F2007 EXAM1 REVIEW