Line integrals - Study guides, Study notes & Summaries
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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 ...
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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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- R483,40
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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 ...
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MAT 21D Final Exam Questions With Multiple Choices & Verified Answers.
- Exam (elaborations) • 5 pages • 2024
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- R233,78
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Arc length in space - correct answer 
 
unit tangent vector formula - correct answer 
 
Find arc length parametrization - correct answer 1. find the arc length (s =xt) 
2. solve for t 
3. plug back into position equation to get r(s) 
 
Formula for curvature - correct answer 
 
unit normal vector formula - correc...
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Student Solutions Manual for Mathematical Methods for Physics and Engineering
- Exam (elaborations) • 546 pages • 2024
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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...
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MAT1512 EXAM PACK 2023 LATEST QUESTIONS AND ANSWERS 1 [TURN OVER] 2 x 0 3 x 9 x2 x QUESTION 1 (a) Determine the following limits (if they exist): (i) (3) (ii) x 2 lim 3 x 1 2 (3) x 3 x 9 (iii) (iv) lim x 2x lim 1 x (3) (3) (v) x
- Exam (elaborations) • 83 pages • 2024
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MAT1512 EXAM PACK 2023 
LATEST QUESTIONS AND ANSWERS 
1 
[TURN OVER] 
2 
x 0 3 
x 9 
x2 x 
 
QUESTION 1 
(a) Determine the following limits (if they exist): 
(i) 
(3) 
(ii) 
x 2 
lim 
3 x 1 
2 
(3) 
x 3 x 9 
(iii) 
(iv) 
lim 
x 2x 
lim 1 x 
(3) 
(3) 
(v) 
x 1 
lim 
1 x 
2x 
(3) 
(vi) 
lim sin t tan 2t 
(3) 
t 0 t 
(b) Use the Squeeze Theorem to determine the following limit: 
5k 2 cos3k 
lim 2 . 
(3) 
 x ...
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CALCULUS FINAL EXAM QUESTIONS WITH VERIFIED ANSWERS
- Exam (elaborations) • 10 pages • 2024
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- R260,78
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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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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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- R779,95
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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:...
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Calculus 1 Final Formulas to know Exam Questions and Answers
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A function is continuous at x=A when... - ANSWER-1.) f(A) exists 
2.) The limit exists 
 -the LHL and RHL are equal 
3.) f(A)=limit 
 
Limit definition of the derivative - ANSWER-the limit as h approaches zero is 
 
[f(x+h)-f(x)]/h 
 
Fundamental Theorem of Calculus I - ANSWER-Derivatives and integrals are inverses 
 
derivative of sin - ANSWER-cos 
 
derivative of cos - ANSWER--sin 
 
derivative of tan - ANSWER-sec^2 
 
derivative of cot - ANSWER-csc^2 
 
derivative of sec - ANSWER-secxtanx 
 
...
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MAT1512 EXAM PACK 2023 LATEST QUESTIONS AND ANSWERS
- Exam (elaborations) • 83 pages • 2023
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- R143,80
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QUESTION 1 
 
(a)	Determine the following limits (if they exist): 
 
 
(i) 
 
 
 
 
 
 
(3) 
 
 
 
(ii) 
 
x 2 
 
lim 
 
3 x 1 
 
 
2 
 
 
 
 
 
(3) 
 
x 3 x 9 
 
 
(iii) 
 
(iv) 
 
lim 
x 	2x 
lim 1 	x 
 
(3) 
 
(3) 
 
 
 
(v) 
 
x 1 
 
lim 
 
1 x 
2x 
 
 
 
(3) 
 
 
 
 
(vi) 
 
lim sin t tan 2t 
 
 
(3) 
 
t 0	t 
 
(b)	Use the Squeeze Theorem to determine the following limit: 
 
5k 2 cos3k 
lim	2	. 
 
 
 
 
(3) 
 
 ...
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Test Bank for Basic Technical Mathematics with Calculus, 12th edition by Allyn J. Washington
- Exam (elaborations) • 1308 pages • 2023
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- R530,73
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Test Bank for Basic Technical Mathematics with Calculus, 12e 12th edition by Allyn J. Washington, Richard Evans. 
 
Full Chapters test bank included - Answers are given at the end of every chapter. 
 
Basic Algebraic Operations 
1.1 Numbers 
1.2 Fundamental Operations of Algebra1.3 Calculators and Approximate Numbers 
1.4 Exponents and Unit Conversions 
1.5 Scientific Notation 
1.6 Roots and Radicals 
1.7 Addition and Subtraction of Algebraic Expressions 
1.8 Multiplication of Algebraic Expressi...
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