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Solutions for Calculus Early Transcendentals, 3rd Edition Briggs (All Chapters included)
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Complete Solutions Manual for Calculus Early Transcendentals, 3rd Edition by William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz ; ISBN13: 9780136880677. (Full Chapters included Chapter 1 to 17)....1. Functions 2. Limits 3. Derivatives 4. Applications of the Derivative 5. Integration 6. A...

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MEDCONNOISSEUR©2024 ✅💯👌😘




SOLUTIONS
MANUAL
CALCULUS




M
E
EARLY TRANSCENDENTALS


D
THIRD EDITION
C
O
N
N

William Briggs
O


Lyle Cochran
S I



Bernhard Gillett
E S
U
R




** Immediate Download ✅
** Swift Response
** All Chapters included
** Directly from the Publisher ✅

MEDCONNOISSEUR©2024 ✅💯👌❤️
MEDCONNOISSEUR©2024✅💯👌❤️

,Contents




M
1 Functions 5




E
1.1 Review of Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Representing Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14




D
1.3 Inverse, Exponential and Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.4 Trigonometric Functions and Their Inverses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Chapter One Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54




C
2 Limits 67




O
2.1 The Idea of Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.2 Definition of a Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.3 Techniques for Computing Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
2.4 Infinite Limits . . . . . . . . . . . . . . . . . .
N
. . . . . . . . . . . . . . . . . . . . . . . . . . 97
2.5 Limits at Infinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
N
2.6 Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
2.7 Precise Definitions of Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
O

Chapter Two Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

3 Derivatives 155
I


3.1 Introducing the Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
S


3.2 The Derivative as a Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
3.3 Rules of Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
S



3.4 The Product and Quotient Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
3.5 Derivatives of Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
E




3.6 Derivatives as Rates of Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
3.7 The Chain Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
U




3.8 Implicit Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
3.9 Derivatives of Logarithmic and Exponential Functions . . . . . . . . . . . . . . . . . . . . . . 258
R




3.10 Derivatives of Inverse Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 270
3.11 Related Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
Chapter Three Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

4 Applications of the Derivative 307
4.1 Maxima and Minima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
4.2 Mean Value Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
4.3 What Derivatives Tell Us . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
4.4 Graphing Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
4.5 Optimization Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
4.6 Linear Approximation and Differentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
4.7 L’Hôpital’s Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
4.8 Newton’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
4.9 Antiderivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
Chapter Four Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456

1

,2 Contents


5 Integration 479
5.1 Approximating Areas under Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479
5.2 Definite Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499
5.3 Fundamental Theorem of Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
5.4 Working with Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536
5.5 Substitution Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546
Chapter Five Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557

6 Applications of Integration 573
6.1 Velocity and Net Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573




M
6.2 Regions Between Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587
6.3 Volume by Slicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
6.4 Volume by Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610




E
6.5 Length of Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620
6.6 Surface Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626




D
6.7 Physical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634
Chapter Six Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644




C
7 Logarithmic, Exponential, and Hyperbolic Functions 661
7.1 Logarithmic and Exponential Functions Revisited . . . . . . . . . . . . . . . . . . . . . . . . 661




O
7.2 Exponential Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669
7.3 Hyperbolic Functions . . . . . . . . . . . . . . . . . . . N . . . . . . . . . . . . . . . . . . . . . 675
Chapter Seven Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687

8 Integration Techniques 693
N
8.1 Basic Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693
8.2 Integration by Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703
O

8.3 Trigonometric Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 722
8.4 Trigonometric Substitutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731
8.5 Partial Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 748
I


8.6 Integration Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763
S


8.7 Other Methods of Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 798
8.8 Numerical Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807
S



8.9 Improper Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 818
Chapter Eight Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833
E




9 Differential Equations 855
U




9.1 Basic Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855
9.2 Direction Fields and Euler’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 861
R




9.3 Separable Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873
9.4 Special First-Order Linear Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . 886
9.5 Modeling with Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894
Chapter Nine Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903

10 Sequences and Infinite Series 911
10.1 An Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 911
10.2 Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 919
10.3 Infinite Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 933
10.4 The Divergence and Integral Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944
10.5 Comparison Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 955
10.6 Alternating Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 963
10.7 The Ratio and Root Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 970
10.8 Choosing a Convergence Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 976
Chapter Ten Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 993

, Contents 3


11 Power Series 1005
11.1 Approximating Functions With Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . 1005
11.2 Properties of Power Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023
11.3 Taylor Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1032
11.4 Working with Taylor Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047
Chapter Eleven Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1061

12 Parametric and Polar Curves 1071
12.1 Parametric Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1071
12.2 Polar Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1088




M
12.3 Calculus in Polar Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1108
12.4 Conic Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1123




E
Chapter Twelve Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1143

13 Vectors and the Geometry of Space 1161




D
13.1 Vectors in the Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1161
13.2 Vectors in Three Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1169




C
13.3 Dot Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1179
13.4 Cross Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1187




O
13.5 Lines and Planes in Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1196
13.6 Cylinders and Quadric Surfaces . . . . . . . . .
N . . . . . . . . . . . . . . . . . . . . . . . . . 1204
Chapter Thirteen Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1219

14 Vector-Valued Functions 1233
N
14.1 Vector-Valued Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1233
14.2 Calculus of Vector-Valued Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1241
O

14.3 Motion in Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1247
14.4 Length of Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1266
I


14.5 Curvature and Normal Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1272
S


Chapter Fourteen Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1283
S



15 Functions of Several Variables 1299
15.1 Graphs and Level Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1299
E




15.2 Limits and Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1311
15.3 Partial Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317
U




15.4 The Chain Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1329
15.5 Directional Derivatives and the Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1340
R




15.6 Tangent Planes and Linear Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1354
15.7 Maximum/Minimum Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1362
15.8 Lagrange Multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1373
Chapter Fifteen Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1382

16 Multiple Integration 1393
16.1 Double Integrals over Rectangular Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1393
16.2 Double Integrals over General Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1400
16.3 Double Integrals in Polar Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1416
16.4 Triple Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1430
16.5 Triple Integrals in Cylindrical and Spherical Coordinates . . . . . . . . . . . . . . . . . . . . 1442
16.6 Integrals for Mass Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1454
16.7 Change of Variables in Multiple Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1465
Chapter Sixteen Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1477

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