MAC 2311/SP07
Practice problems(I will update these suggested problems again on Sunday, 29th April!!!)
Suggested practice problems(you should practice more exercises from the book):
Before practicing problems, make sure you understand the followings concepts, rules, theorems/tests and
explore ideas:
Limit; Continuity; Derivative; Find derivative using limit process; Differentiation rules; Increasing and
decreasing Theorem/Test; Relative Maximum and Minimum Theorem/Test; The second derivative Test;
Extreme Value Theorem; Antiderivative; Fundamental Theorem of Calculus; Integration Rules; etc(keep
in mind that all the tests we used to check relative max/min and absolute max/min, most book referred it
as theorems)
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
 1  2x
7x
Find
for
2 x 0
for
for
0x2
2 x4
lim F ( x)
x 5
x  25
and
x 0
iv)
lim x 0
lim F ( x)
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 it was
0.17 h
. Find and interpret lim A( h).
h
h2  2
x0
 x  1,

SE3. Consider f ( x)    1, x  [0,1)
. Where is f (x ) not continuous and explain why? Sketch
2
 x
x 1

the graph of f (x ) .
injected is given by A( h) 
SE4. Find the derivative of the following function using the limit process:
f ( x) 
1
x 1
SE5. Find the derivatives using Chain Rule:
(ii) g ( x) 
(i) f ( x)  (3x  2 x 2 ) 3
SE6. Find the derivatives
a.
y  ln(ln x)  e x
7
(2 x  3) 2
dy 
dx of each of the following function.
2
2
c.
y  e ln x  3x 7
2
d. y  x
e  e x
MAC 2311 FINAL PRACTICE PROBLEMS - M. RAHMAN
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y
4 x2  x
3
3
.
(2 x x3 )
e.
f. y  ln( 3) 3
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)
 e2
-------------------------------------------------------------------------Section 4.5 -# 4, 6, 8, 12, 16, 18, 22, 24, 34, 39
Section 4.6 # 4, 6, 8, 10, 12, 14, 16, 18, 22, 26
Section 5.1 # 6, 10, 12, 16, 20, 22, 25, 37, 39
Section 5.2 # 6, 10, 12, 21, 26
Section 5.3 # 4, 6, 8, 16, 20, 22, 24, 25, 30, 34, 40
Section 5.4 # 13, 14, 20
Section 6.1 # 4, 10, 14, 16, 22, 24, 25
Section 6.2 # 6, 24, 30
Section 6.3 # 4, 6, 14, 16, 20, 22, 28
Section 6.4 # 6, 8, 14, 18, 19
Applications to life sciences/others:
PAGE 249: EX. 50 (Learning)
PAGE 276: EX. 40, 41(Drug concentration)
PAGE 289: EX38 (Milk consumption)
PAGE 303: EX. 61, 66(Drug concentration)
PAGE 315: EX. 44 (Neuron communication)
PAGE 330: EX. 46 (Gasoline Mileage)
PAGE 332-342: EXAMPLE #1, 3, 4, Exercise 6(Pollution), 24, 30, 38
PAGE 349-356: Example 1, 2, 3, Exercise 18(Learning skill), 22, 30
--------------------------------------------------------------------------------------7.1 # 12, 16, 20, 22, 28, 32, 36, 46, 52
7.2 # 6, 8, 10, 14, 16, 20, 24, 34, 37
7.3 # 15, 16, 18, 20
7.4 # 8, 12, 20, 22, 25, 28, 59(spread of an oil leak), 70(oil consumption)
7.5 # 2, 4, 6,10
Read all sections, do hw & quizzes, and read class notes!!!
SP2007 Copyright 2007 University of North Florida
MAC 2311 FINAL PRACTICE PROBLEMS - M. RAHMAN
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SP2007 Copyright 2007 University of North Florida