Line integrals Study guides, Study notes & Summaries
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![Multivariable Calculus Notes: Integrals](/docpics/3113211/64bc52d14edac_3113211_121_171.jpeg)
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Multivariable Calculus Notes: Integrals
- Class notes • 24 pages • 2023
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Notes for MIT OpenCourseware MATH 18.02 lectures by Denis Auroux and Calculus by James Stewart. Includes double integrals, line integrals, Green's Theorem, and Stokes' Theorem.
![Test Banks For Essential Calculus 2nd Edition by James Stewart, 9781133112297, Chapter 1-13 Complete Guide](/docpics/63c79cc1e516f_2269802.jpg)
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Test Banks For Essential Calculus 2nd Edition by James Stewart, 9781133112297, Chapter 1-13 Complete Guide
- Exam (elaborations) • 298 pages • 2023
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Essential Calculus 2nd Edition 
 
2297 
 
0875 
 
0, 3, 4, 0, 2467, 3011, 9067, 6609 
 
1: Functions and Limits 
 
1.1: Functions and Their Representations 
 
1.2: A Catalog of Essential Functions 
 
1.3: The Limit of a Function 
 
1.4: Calculating Limits 
 
1.5: Continuity 
 
1.6: Limits Involving Infinity 
 
2: Derivatives 
 
2.1: Derivatives and Rates of Change 
 
2.2: The Derivative as a Function 
 
2.3: Basic Differentiation Formulas 
 
2.4: The Product and Quotient Rules 
 
2.5: The Chain ...
![MAT2615 EXAM PACK 2023](/docpics/63e67ea7e2437_2357926.jpg)
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MAT2615 EXAM PACK 2023
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INTRODUCTION 
Dear Student 
Welcome to MAT2615. We trust that you will find the mathematics studied in this module interesting 
and useful, and that you will enjoy doing it. 
THIS TUTORIAL LETTER CONTAINS INFORMATION TO FACILITATE YOUR STUDIES. PLEASE 
READ IT CAREFULLY AND KEEP IT FOR FUTURE REFERENCE. 
The delivery mode for this module is “blended”, which means that only some study material will be 
printed and posted to you. All study material which may include additional material will be...
![Test Banks For Essential Calculus 2nd Edition by James Stewart, 9781133112297, Chapter 1-13 Complete Guide](/docpics/63c8104339301_2271637.jpg)
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Test Banks For Essential Calculus 2nd Edition by James Stewart, 9781133112297, Chapter 1-13 Complete Guide
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Essential Calculus 2nd Edition 
 
2297 
 
0875 
 
0, 3, 4, 0, 2467, 3011, 9067, 6609 
 
1: Functions and Limits 
 
1.1: Functions and Their Representations 
 
1.2: A Catalog of Essential Functions 
 
1.3: The Limit of a Function 
 
1.4: Calculating Limits 
 
1.5: Continuity 
 
1.6: Limits Involving Infinity 
 
2: Derivatives 
 
2.1: Derivatives and Rates of Change 
 
2.2: The Derivative as a Function 
 
2.3: Basic Differentiation Formulas 
 
2.4: The Product and Quotient Rules 
 
2.5: The Chain ...
![Solutions For Calculus, Early Transcendental Functions, 8th Edition Larson (All Chapters included)](/docpics/3880319/655da680bfeeb_3880319_121_171.jpeg)
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Solutions For Calculus, Early Transcendental Functions, 8th Edition Larson (All Chapters included)
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Complete Solutions Manual for Calculus, Early Transcendental Functions, 8th Edition by Ron Larson, Bruce H. Edwards , 9780357759325. Full chapters included Chapter 1 to 16. 
1. Preparation for calculus. 2. Limits and their properties. 3. Differentiation. 4. Applications of differentiation. 5. Integration. 6. Differential equations. 7. Applications of integration. 8. Integration techniques and improper integrals. 9. Infinite series. 10. Conics, parametric equations, and polar coordinates. 11. Vec...
![Calculus: Single and Multivariable, 7th Edition by Deborah Hughes-Hallett, William G. McCallum, and Andrew M. Gleason, et al. All Chapters 1-21. (Complete Download). TEST BANK.](/docpics/63ea7543af662_2367021.jpg)
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Calculus: Single and Multivariable, 7th Edition by Deborah Hughes-Hallett, William G. McCallum, and Andrew M. Gleason, et al. All Chapters 1-21. (Complete Download). TEST BANK.
- Exam (elaborations) • 539 pages • 2023
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Calculus: Single and Multivariable, 7th Edition by Deborah Hughes-Hallett, William G. McCallum, and Andrew M. Gleason, et al. All Chapters 1-21. (Complete Download). TEST BANK. 
 
Calculus: Single and Multivariable, 7th Edition by Deborah Hughes-Hallett, William G. McCallum, and Andrew M. Gleason, et al. All Chapters 1-21. (Complete Download). TEST BANK. TABLE OF CONTENTS C hapter 1: A Library of Functions Chapter 2: Key Concept: The Derivative Chapter 3: Short-Cuts to Differentiation Chapter 4:...
![Math 215: Final Exam 2024 with 100% correct answers](/docpics/4902329/660c671d8112c_4902329_121_171.jpeg)
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Math 215: Final Exam 2024 with 100% correct answers
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what is the equation for finding the mass of a function on a line integral? correct answersm=∫a→b p[x(t),y(t),z(t)]∙[x'(t)²+y'(t)²+z'(t)²]^(1/2) dt 
 
how do you find moment about the x-axis correct answersMyz=∫a→b x∙p(x,y,z) ds 
 
NOTE: the x/y/z in p(x,y,z) gets parameterized to t before solving. use t limits to solve 
 
how do you find moment about the y-axis correct answersMxz=∫a→b y∙p(x,y,z) ds 
 
NOTE: the x/y/z in p(x,y,z) gets parameterized to t before solving. us...
![Student Solutions Manual for Mathematical Methods for Physics and Engineering](/docpics/4897236/660bee655e596_4897236_121_171.jpeg)
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Student Solutions Manual for Mathematical Methods for Physics and Engineering
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Preface page ix 
1 Preliminary algebra 1 
2 Preliminary calculus 17 
3 Complex numbers and hyperbolic functions 39 
4 Series and limits 55 
5 Partial differentiation 71 
6 Multiple integrals 90 
7 Vector algebra 104 
8 Matrices and vector spaces 119 
9 Normal modes 145 
10 Vector calculus 156 
11 Line, surface and volume integrals 176 
v 
CONTENTS 
12 Fourier series 193 
13 Integral transforms 211 
14 First-order ODEs 228 
15 Higher-order ODEs 246 
16 Series solutions of ODEs 269 
17 Eigenfuncti...
![Department of Mathematics](/docpics/3987537/657306f4613c4_3987537_121_171.jpeg)
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Department of Mathematics
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Department of 
Mathematics 
Courses of Study: 
Minor 
Major (B.A.) 
Combined B.A./M.A 
Master of Arts 
Doctor of Philosophy 
Objectives 
Undergraduate Major 
As our society becomes more technological, it is more affected by 
mathematics. Quite sophisticated mathematics is now central to 
the natural sciences, to ecological issues, to economics, and to 
our commercial and technical life. A student who takes such 
general level courses as MATH 5, 8, 10, 15, or 20 will better 
understand the world ...
![CALCULUS FINAL EXAM QUESTIONS WITH VERIFIED ANSWERS](/docpics/5348835/66489f1501e48_5348835_121_171.jpeg)
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CALCULUS FINAL EXAM QUESTIONS WITH VERIFIED ANSWERS
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evaluate the integral 2/1, ln(x)/x dx - ANSWER-(ln2)^2/2 
 
consider the function f(x)=x^4-4x^3. which of the following is NOT true - ANSWER-f has a local extrema at x=0 and x=3 
 
find the work done by a force F=sqroot 2x+1 N to move an object along a straight path from a distance of 0 meters to a distance of 4 meters - ANSWER-26/3 J 
 
an object is moving along the x-axis. Let s(t), v(t) and a(t) be functions giving the position, the velocity, and the acceleration of the object at time t. whic...
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