MAC 2311/SP07
Exam1 Review/Sample Exercises(SE)
SE1. Find the limit(if it exists).
x2  x  2
(i ) lim 2
x2 x  x  6
iii ) F ( x)  x  3
(ii ) lim
x 5
for
2 x 0
for
for
0x2
2 x4
 1  2x
7x
Find
lim F ( x)
x 5
x  25
lim F ( x)
and
x 0
iv)
lim x 0
x2
3 x  3
x
v)
lim x
2( x  sin x)
x
SE2. (Drug Concentration) The concentration of a drug in a patient’s bloodstream h hours after
0.17 h
. Find and interpret lim A( h).
it was injected is given by A( h)  2
h
h 2
x0
 x  1,

SE3. Consider f ( x)    1, x  [0,1)
. Where is f (x ) not continuous and explain why? Sketch
 x2
x 1

the graph of f (x ) .
SE4. Find the derivative of the following function using the limit process:
1
x 1
SE5. Find the derivatives using Chain Rule:
f ( x) 
(ii) g ( x) 
(i) f ( x)  (3x  2 x 2 ) 3
SE6. Find the derivatives
a.
y  ln(ln x)  e x
y
e.
dy 
dx of each of the following function.
2
4 x2  x
3
3
.
7
(2 x  3) 2
2
c.
y  e ln x  3x 7
3
f. y  ln( 3) 3(2 x x )  e 2
SE7. Applications to life sciences/others:
PAGE 160: EX. 32(Pregnancy)
PAGE 161: EX. 37(Production)
PAGE 189: EX. 48(Temperature)
PAGE 231: EX. 50(Blood Sugar Level)
PAGE 222: EX. 38(Bacteria Population)
PAGE 232: EX. 54(Oil Pollution)
PAGE 239: EX. 32(Population Growth)
2
d. y  x
e  e x
MAC 1147 EXAM 1 - M. RAHMAN
Read example from all sections, hw, quizzes, and class notes.
F2006 Copyright 2006 University of North Florida
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