Derivative and integrals Study guides, Class 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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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...
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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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Mathematics 114 summaries
- Summary • 80 pages • 2022
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Aesthetic digital concise summaries of all the theory and some examples you need to know for mathematics 114. 
The whole semester's content for mathematics 114 is summarised. 
Self-study: Revision of coordinate geometry & straight lines 
These are topics that you should be familiar with from school. Some students forget some of this material by the time they start their first year, and therefore need to revise them. These topics are all required for Calculus topics later on. 
 
Week 1: Numbers,...
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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:...
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MAT1512 Assignment 9 2021 (Oct/Nov 2020 exam)
- Other • 24 pages • 2021
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UNISA MAT1512 Calculus A Assignment NINE of 2021 solutions. October November 2020 past paper. 
Where possible, alternative methods are used. 
Topics covered: 
Limits at a finite point. 
Limits at plus/minus. 
Limits from the left/right hand side. 
Continuity. 
Curve sketching. 
Integrals. 
Integration. 
Simplify then integrate. 
u-substitution. 
Definite/indefinite integrals. 
Area in between curve. 
Initial value Ordinary differential equations. 
Differentiation. 
Derivatives. 
Derivative from ...
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Calculus 1 Final Formulas to know Exam Questions and Answers
- Exam (elaborations) • 4 pages • 2024
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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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Math 475: Partial Differential Equations
- Exam (elaborations) • 19 pages • 2023
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Math 475: Partial Differential Equations 
Shereen Elaidi 
Fall 2019 Term 
Contents 
1 Introduction 2 
1.1 Domains and Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
1.1.1 What are the main boundary conditions? . . . . . . . . . . . . . . . . . . . . . 3 
1.2 Classification of PDEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
2 Diffusion 4 
2.1 Derivation and Setting Up (n = 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
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MAT1512 EXAM PACK 2023 LATEST QUESTIONS AND ANSWERS
- Exam (elaborations) • 83 pages • 2023
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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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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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