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CHAPTER 1 LIMITS OF FUNCTIONS8 F o% S: M0 q, ?
Section 1-1 Limits8 a* ^0 ] `/ k
Section 1-2 One-Sided Limit7 I' i W! f, l5 S
Section 1-3 Continuity$ _ z' \) V, W& n1 T$ ^
Section 1-4 A Limit at Infinity and Infinite Limit
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CHAPTER 2 DERIVATIVE
2 h$ V0 Y) i5 x4 H: VSection 2-1 Definition of Derivative
( z" S* ]! Y! `+ j9 {3 sSection 2-2 The Rule of Differentiation, n2 g. o6 a: U% n! i' |4 x2 B
Section 2-3 Chain Rule and Implicit Differentiation
) F' r$ g! V# G/ R2 v. n0 J1 rSection 2-4 Derivatives of Exponential and Logarithmic F
9 E. R' R2 y+ [0 C- TSection 2-5 Numerical Approximate –Differentials
/ V' e+ |. s& }) aSection 2-6 Derivatives of Trigonometric Functions i3 E+ [# I' U: c3 a
Section 2-7 Derivatives of Inverse Trigonometric F1 O0 X5 F; x/ L& i
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CHAPTER 3 APPLICATIONS OF DERIVATIVES
L3 w! }' c9 i1 f3 @Section 3-1 The Mean Value Theorem and its Applications9 [. i/ y/ @# f8 `# t
Section 3-2 Increasing and Decreasing Functions
0 Y$ V# r4 H7 s( QSection 3-3 Maximum and Minimum Values R) G/ r6 [* C2 L+ l/ c. t
Section 3-4 The Max -Min Problems
8 N6 R, X# t9 s4 s& mSection 3-5 Concavity and Points of Inflection # v2 M# H0 g8 z( ?; S2 s) f6 T1 M
Section 3-6 Asymptotes
1 o2 T( W& d7 |5 L8 USection 3-7 Sketching curve6 `8 D# M3 Z! m: U- Q
Section 3-8 L' Hopital's Rule! F0 I2 l* G/ A9 |
Section 3-9 Taylor Series
, e$ z/ {, I5 r! i7 NSection 3-10 Applications In Marginal Analysis
4 ~: X$ L) N. h7 d$ }/ lSection 3-11 Elasticity9 Q9 T: l, J7 H2 l
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CHAPTER 4 THE INDEFINITE INTEGRALS
1 N) J- x, Z D) ^7 r3 R; k7 ISection 4-1 Antiderivative and The Indefinite Integrals I. a2 k" r/ w. n! [4 @5 p
Section 4-2 Integration by Changing Variables0 v, b5 m* i, R, f6 e) g2 d
Section 4-3 Integration by Parts
6 g0 y9 G; F, _Section 4-4 The Trigonometric Integrals9 D1 T. p$ t- n4 c3 H) K, C
Section 4-5 The Integration by Partial Fractions
* G y9 k, Z" H ESection 4-6 Trigonometric and Half-Angle Substitution! I6 |, l6 ?5 I; F+ H
( Y8 t& ~0 D+ B2 bCHAPTER 5 THE DEFINITE INTEGRALS$ ]" @( j r; C' Q0 U) `- u- u
Section 5-1 Areas and the Definition of Definite Integral' `: Y' i& T. E' z
Section 5-2 The Fundamental Theorem of Calculus$ @2 r7 U2 J: C
Section 5-3 The Approximate Integration5 U+ @0 o" D1 m$ m6 [9 W
Section 5-4 The Improper Integrals
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! J/ h, b/ V+ ?* e* \" g. g9 ZCHAPTER 6 APPLICATIONS OF INTEGRATION
: W j; X0 P1 {! v) B. TSection 6-1 Areas between Curves8 q6 u* O$ u3 T; ^
Section 6-2 Areas in Polar Coordinates" s* X4 l$ e! W" [
Section 6-3 Arc Length ^7 C0 ^0 g' {- x* L* _
Section 6-4 Volumes and The Volumes of Revolution5 l& C' ?' w( X) z- S9 B
Section 6-5 Area of a Surface of Revolution
$ \ N' P4 m# Q& YSection 6-6 Centroid of A Plane Region8 G! E" Y$ x$ e/ c, o! ]
Section 6-7 Work and The Problems of The Engineering
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CHAPTER 7 PARTIAL DERIVATIVES
' h% j9 k; T8 f- ?( D* y3 BSection 7-1 Limits and Continuity* p: M* {" ^* n$ Q" S( `: h0 m
Section 7-2 Partial Derivatives6 Q; X4 s5 N( I. A
Section 7-3 The Differentials and Chain Rules
) g9 W+ W7 q: q% RSection 7-4 Extrema of Functions of Two Variables
, L- U3 y: O5 l& A/ O2 aSection 7-5 Directional Derivatives, Gradient and Tangent Plane, }7 {6 [# y& k
+ z2 |1 y' v; sCHAPTER 8 MULTIPLE INTEGRALS. n% `4 F$ b5 c3 m/ f0 \
Section 8-1 Integrals over a Rectangle
3 M% C' {& A' _) [Section 8-2 Integrals over a Region, ]2 t5 o& K' q) B+ j& Q) D
Section 8-3 Three-Dimensional Iterated Integrals/ Y. {" K" l0 a% M
Section 8-4 Multiple Integration in Polar, Cylindrical and Spherical Coordinates
$ p% O9 c3 |% {2 @2 b8 l, W8 sSection 8-5 Applications of Multiple Integrals
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