Calculus the classic edition

1186 Pages·1991·140.113 MB·English

by  Earl W. Swokowski

FORMUlAS FOR DERIVATIVES FORMUlAS FOR INTEGRALS
D"c "" 0 fudv=w,- fCdu
2 D,,(u + 11)= DJtu + D"v
2 fu~du= _'_'I'''1 +c'n#= - I
n+!
3 D .. (uv) = II D"II + II D"u
('4) _II II -II II 3 fldu =lnlul+c
• D - - Dx Dx " v
'" II v2 •
f e"du=e"+C
5 D. /(g(X)) ~ J'(g(.,))g'(x)
• 5 Sa~ du= -'-a"+C
D" II' = nu"- I Ox II In a
•
7 D" e" "" e" D~ II f Sin udu = -cos u + C
• f
D"o" = a"ln (l D"u 7 cos II du = sin u + C V
• I
D.ln lul~ - D.u • f
. u secl udu = tan u + C
I • Jese
I. D. 'o .. lul ~ -u,n-a D.u l udu = -COl u + C
f
11 D" sin II = cos II Ox II I. sec II tan u du = sec u + C
12 DJ/cos u = -sinuD"u
11 f CSC liCOludu = -cscu+C
1I.3 Dlt tan II = sec1 110" II f
12 Ian II till = - In Ic os II I + C
D"cotu= - csc1u D"u
J
13 cot u du = In Is in u I + C
15 D" sec II = sec II tan II D" II
f
I. D"csc u= -csc ucotuDJ<u " sec u du = In Is ec II + tan II I + C
S
17 D" SI. n - l 1/ = ~I _I Du2 r oll 15 esc II dll = In lese II - COl ul + C
I.
l. f
- I 1 du=sin-I~+C
D cos-I u= D.u Ja1 ul a
JI ~
J I I u
I 17 21du= - lan- I - +C
19 D" tan-I u = -, --2 D"u a + II a a
+u
f
2. O see-Iu= I 18 du = ~ sec- L II + C
• ~ D.U u,.illl _ a1 a a
II 1/2 - I
------------------------
el Mar B
You S e $ At 0
FORMULAS FROM GEOM
,')erving Del Mar Ccdege Student,
Since 1.9501
<t:; '@'\l1f» ; curved surface area S; altitude h
He"dquarters for l>.h-w & US0d Textbooks
RIGHT TRIANGLE TRIANGLE
2501
Ay~rs
884-1866
/ 0 :l
b 5
J3
J3
Pythagorean Theorem: c2 = a2 + b2 A = 1bh C=a+b+c h= - 5 A = 52
2 4
RECTANGLE PARALLELOGRAM TRAPEZOID
a
O~ih
'---LL /
b
A = lw C = 21 + 2w A = bh
CIRCLE CIRCULAR SECTOR
5
C = 2nl' 5 = 1'8
RECTANGULAR BOX SPHERE RIGHT CIRCULAR CYLINDER
I
I r I
~
v = lwh S = 2(hl + lw + hw) S = 2nrh
i-,
RIGHT CIR:C-U-LA-R- 1CO NE FRUSTUM OF A CONE PRISM
~
I r I r'-_~_41"'"
I h --~t
~----± 1 _1 I h
I __ d_f
I I I I
I I I I
~r~ ~R~
S = nrJr2 + h2 V = tnh(r2 + rR + R2) V = Bh with B the area of the base

FIFTH EDITION
EARL W. SWOKOWSKI
Marquette University
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Lihrary of Congress Cataloging-in-Puhlication Data
SWO"o\\:;"I, Earl William,
Caiculu,/Llrl \\, SIIOJ,;O\\SJ,;I-'i,h cd,
I', erli,
Include, index,
ISB\I tJ-'i.'4-92-192-1
I, Cllculm. 2 C;ellIl1etn, Anal\ tic L S\\()kow:;J,;i, Earl William, Cliculu., \11th
anaivtlc ~e()Il1etry II. Title,
Q.-\"O"S)-I 1l)()1 l)()--I II Xn
'i1'i.IS-dl'20
L
Dedicated to the memory of
my mother and father,
Sophia and John Swokowski

CONTENTS
PREFACE xv
FOR THE STUDENT xx iii
CHAPTER 1 PRECALCULUS REVIEW
1.1 Algebra 2
1.2 Functions 1 4
1.3 Trigonometry 26
CHAPTER 2 LIMITS OF FUNCTIONS 39
2.1 Introduction to Limits 40
2.2 Definition of Limit 5 1
2.3 Techniques for Finding Limits 58
2.4 Limits Involving Infinity 68
2.5 Continuous Functions 77
2.6 Review Exercises 88
vii i CONTENTS
CHAPTER 3 THE DERIVATIVE 89
3.1 Tangent Lines and Rates of Change 90
3.2 Definition of Derivative 98
3.3 Techniques of Differentiation 109
3.4 Derivatives of the Trigonometric Functions 1 1 8
3.5 Increments and Differentials 127
3.6 The Chain Rule 137
3.7 Implicit Differentiation 146
3.8 Related Rates 152
3.9 Review Exercises 162
-CH-A-PTER 4 APPLICATIONS OF THE DERIV-A-TIV-E 165
4.1 Extrema of Functions 166
4.2 The Mean Value Theorem 177
4.3 The First Derivative Test 183
4.4 Concavity and the Second Derivative Test 191
4.5 Summary of Graphical Methods 199
4.6 Optimization Problems 207
4.7 Rectilinear Motion and Other Applications 220
4.8 Newton's Method 232
4.9 Review Exercises 236
CHAPTER 5 INTEGRALS 239
5.1 Antiderivatives and Indefinite Integrals 240
5.2 Change of Variables in Indefinite Integrals 250
5.3 Summation Notation and Area 257
5.4 The Definite Integral 266
5.5 Properties of the Definite Integral 275
5.6 The Fundamental Theorem of Calculus 282
5.7 Numerical Integration 292
5.8 Review Exercises 300