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, REFERENCE page 1
ALGEBRA GEOMETRY
Arithmetic Operations Geometric Formulas
Cut here and keep for reference
a c ad 1 bc b
asb 1 cd − ab 1 ac 1 − Formulas for area A, circumference C, and volume V:
d bd
a Triangle Circle 2 Sector of Circle
a1c a c b a d ad A − 1 bh A− r A − 1 r2
− 1 − 3 − 2 2
b b b c b c bc 1
−
d 2 ab sin C−2 r s − r s in radiansd
Exponents and Radicals
m
a r s
x h
xmx n
− x m1n − x m2n ¨
xn r
¨
m n mn 1 b
sx d − x x2n − r
SD
xn
x n x n
sxydn − x n y n −
y yn
Sphere Cylinder Cone
Î
m
x m yn − ns x m − (ns x )
n
x 1yn − s x V − 4 r3 V − r 2h V − 1 r 2h
n
s xy − sn x ns y n − n 3 3
y yn
x sx 2
A−4 r A − rsr 2 1 h2
s
r
Factoring Special Polynomials
r h
x 2 2 y 2 − sx 1 ydsx 2 yd h
x 3 1 y 3 − sx 1 ydsx 2 2 xy 1 y 2d r
x 2 y − sx 2 ydsx 1 xy 1 y d
3 3 2 2
Binomial Theorem Distance and Midpoint Formulas
sx 1 yd2 − x 2 1 2xy 1 y 2 sx 2 yd2 − x 2 2 2xy 1 y 2 Distance between P1sx1, y1d and P2sx 2, y2d:
sx 1 yd3 − x 3 1 3x 2 y 1 3xy 2 1 y 3
sx 2 yd3 − x 3 2 3x 2 y 1 3xy 2 2 y 3 d − ssx 2 2 x1 d2 1 s y2 2 y1 d2
2 1d
S
nsn
sx 1 ydn − x n 1 nx n21 y 1
2
x n22 y 2
Midpoint of P1 P2:
x1 1 x 2 y1 1 y2
2 , 2 D
1…1 SD n
k
xn2k yk 1 … 1 nxy n21 1 y n
SD
Lines
n nsn 2 1d … sn 2 k 1 1d
where k − 1?2?3?…?k Slope of line through P1sx1, y1d and P 2sx 2, y2d:
Quadratic Formula y2 y1
m− x 2x
2b 6 sb 2 2 4ac 2 1
If ax 1 bx 1 c − 0, then x −
2
.
2a
Point-slope equation of line through P1sx1, y1d with slope :
Inequalities and Absolute Value
y 2 y1 − msx 2 x1 d
If a , b and b , c, then a , c. If a
, b, then a 1 c , b 1 c. Slope-intercept equation of line with slope and y-intercept b:
If a , b and c . 0, then ca , cb. If a
y − mx 1 b
, b and c , 0, then ca . cb. If a . 0,
then Circles
|x | − a means or Equation of the circle with center sh, kd and radius :
|x | , a means 2a , x , a
sx 2 hd2 1 s y 2 kd2 − r 2
|x | . a means x . a or x , 2a
Copyright 2021 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage L earning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
, REFERENCE page 2
TRIGONOMETRY
Angle Measurement Fundamental Identities
radians − 1808 1 1
csc − sec −
sin cos
180° s
18 − rad 1 rad − r sin cos
180 ¨
tan − cot −
s−r cos sin
r
s in radiansd 1
cot − sin2 1 cos2 − 1
tan
Right Angle Trigonometry 1 1 tan2 − sec 2 1 1 cot2 − csc2
opp hyp
sin − csc − sins2 d − 2sin coss2 d − cos
cos −
hyp
adj
sec −
opp
hyp
hyp
opp tans2 d − 2tan sin S D 2 − cos
hyp adj ¨ 2
S D S D
adj
opp adj
tan − cot − cos 2 − sin tan 2 − cot
adj opp 2 2
Trigonometric Functions
y r
sin − csc − y
r y sin A sin B sin C a
x r (x, y) a − b − c
cos − sec − r C
r x c
y x ¨
tan − cot − The Law of Cosines
x y x b
a 2 − b 2 1 c 2 2 2bc cos A
Graphs of Trigonometric Functions b 2 − a 2 1 c 2 2 2ac cos B
y y y y=tan x c 2 − a 2 1 b 2 2 2ab cos C A
y=sin x y=cos x
1 1
π 2π Addition and Subtraction Formulas
2π
x π 2π x x sinsx 1 yd − sin x cos y 1 cos x sin y
π
_1 _1 sinsx 2 yd − sin x cos y 2 cos x sin y
cossx 1 yd − cos x cos y 2 sin x sin y
y y=csc x y y=sec x y y=cot x cossx 2 yd − cos x cos y 1 sin x sin y
1 1 tan x 1 tan y
tansx 1 yd − 1 2 tan x tan y
π 2π x π 2π x π 2π x tan x 2 tan y
tansx 2 yd − 1 1 tan x tan y
_1 _1
Double-Angle Formulas
sin 2x − 2 sin x cos x
Trigonometric Functions of Important Angles
cos 2x − cos 2 x 2 sin2 x − 2 cos 2 x 2 1 − 1 2 2 sin2 x
radians sin cos tan
2 tan x
08 0 0 1 0 tan 2x −
1 2 tan2 x
308 y6 1y2 s3y2 s3y3
458 y4 s2y2 s2y2 1 Half-Angle Formulas
608 y3 s3y2 1y2 s3
1 2 cos 2 x 1 1 cos 2x
908 y2 1 0 — sin2 x − 2 cos 2x − 2
Copyright 2021 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
, CALCULUS
E A R LY T R A N S C E N D E N TALS
NINTH EDITION
M e t r i c Ve r s i o n
JAMES STEWART
McMASTER UNIVERSITY
AND
UNIVERSITY OF TORONTO
DANIEL CLEGG
PALOMAR COLLEGE
SALEEM WATSON
CALIFORNIA STATE UNIVERSITY, LONG BEACH
Australia • Brazil • Mexico • Singapore • United Kingdom • United States
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, This is an electronic version of the print textbook. Due to electronic rights restrictions, some third
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, Calculus: Early Transcendentals, Ninth Edition, © 2021, 2016 Cengage Learning, Inc.
Metric Version WCN: 02-300
James Stewart, Daniel Clegg, Saleem Watson ALL RIGHTS RESERVED. No part of this work covered by the copyright herein
may be reproduced or distributed in any form or by any means, except as
Metric Version Prepared by Anthony Tan and permitted by U.S. copyright law, without the prior written permission of the
Michael Verwer both at McMaster University copyright owner.
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Print Number: 01 Print Year: 2019
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,Contents
Preface x
A Tribute to James Stewart xxii About
the Authors xxiii
Technology in the Ninth Edition xxiv To
the Student xxv
Diagnostic Tests xxvi
A Preview of Calculus 1
1 Functions and Models 7
1.1 Four Ways to Represent a Function 8
1.2 Mathematical Models: A Catalog of Essential Functions 21
1.3 New Functions from Old Functions 36
1.4 Exponential Functions 45
1.5 Inverse Functions and Logarithms 54
Review 67
Principles of Problem Solving 70
2 Limits and Derivatives 77
2.1 The Tangent and Velocity Problems 78
2.2 The Limit of a Function 83
2.3 Calculating Limits Using the Limit Laws 94
2.4 The Precise Definition of a Limit 105
2.5 Continuity 115
2.6 Limits at Infinity; Horizontal Asymptotes 127
2.7 Derivatives and Rates of Change 140
W RITING PRO JEC T • Early Methods for Finding Tangents 152
2.8 The Derivative as a Function 153
Review 166
Problems Plus 171
iii
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, THOSE WERE PREVIEW PAGES
TO DOWNLOAD THE FULL PDF
CLICK ON THE L.I.N.K
ON THE NEXT PAGE
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.