(Ebook) BUSINESS CALCULUS Notebook Practicing Calculus Statistics and Technology 2nd Edition by Independently Published ISBN 9798729023608 8729023602

(Ebook) BUSINESS CALCULUS Notebook Practicing Calculus Statistics and Technology 2nd Edition by Independently Published ISBN 9798729023608 8729023602

(Ebook) BUSINESS CALCULUS Notebook Practicing Calculus Statistics and Technology 2nd Edition by Independently Published - Ebook PDF Instant Download/Delivery: 9798729023608 ,8729023602
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ISBN 10: 8729023602
ISBN 13: 9798729023608
Author: Independently Published

(Ebook) BUSINESS CALCULUS Notebook Practicing Calculus Statistics and Technology 2nd Edition Table of contents:

CHAPTER-1. LIMITS
1.1. The Idea of a Limit
Examples of Limit Evaluation, an introductory view about the evaluation tactics:
1. Find the limit (š value) as ™ approaches Ύ of the linear equation: š=θ™+φ
2. Find the limit (š value) as ™ approaches β of the quadratic function: š=β,™-β.+Ύ1+β
3. Find the limit (š value) as ™ approaches θ of the rational equation: š=,β-θ+™.
4. Prove that ,ŠŽ-™→Υ. ,™+θ-Ύ+,™..=Ϗ
5. Find the limit as ™ approaches Ϗ of the rational expression using numeric and graphic interpretation:
6. Find the limit as ™ approaches Υ of the rational expression:
7. Estimate the value of the limit as ™ approaches ώ of the rational expression using numeric and graphic interpretation:
8. Estimate the value of the limit when the function exists in one side, using graphic interpretation:
9. Estimate the value of the limit when the function exists in one side, use graphic interpretation:
1.2. Formal Limit Definition
Steps for proving that ŠŽŠ• exist:
Steps for proving that ,ŠŽ-™→. ‡,™.=∞ exist (Two-Side Infinite Limit):
Example 1. Finding ̹ for a given ̺:
Example 2. Finding ̹ for a given ̺:
Example 3. Prove that ,ŠŽ-™→−Ϗ. ,,™-β.+θ.=Υ.
1.3. Determining Limits and Algebraic Properties of Limits
Examples (accurate the limits evaluation applying some algebra simplification when possible:
Homework Topics 1.1, 1.2, and 1.3
1.4. Continuity, Intermediate Value Property, and One-Side Limits.
1.4.1. Continuity:
Some well-known facts related to continuity:
1.4.2. Intermediate Value Property of Continuous Function.
1.4.3. Bisection Algorithm for Approximating Roots
Example:
Method-1 (inaccurate approximation):
Method-2 (accurate approximation using bisection method):
1.4.4. Examples of Discontinuous Function and one Side Limit:
1.5. Limits at the Infinity (Analyzing also One Side Limit)
Consider the function ‡(™)=,βώ,™-β.+™+β-,™-β.. for “large” values of x.
Examples
Homework Topic 1.4 and 1.5.
In 31-34 exercises find one-side limit, verify your answer with Mathematics or Wolfram Alpha.
In the next exercises decide if the given function is continuous at the given point.
In the next exercises find the limit at the infinity
1.6. Example of Limit Calculation Using Technology
PROJECT-1. Find the Limit Using technology.
You can print the Project from Professor Prieto-Valdes Web-page.
Example 1
Example 2.
Example 3.
Example 4:
Example 5:
Example 6:
PRACTICING QUIZ-1. Limits
CHAPTER-2. THE DERIVATIVE AND DIFFERENTIATION
2.1. Definition of Derivative
2.1.1. Linear Function and Slope of the Line:
2.1.2. Slope of the Secant Line
,Ž=,∆š-∆™.=-,‡,™+∆™.−‡,™.-∆™..
2.1.3. Slope of the Tangent Line:
The next illustration serves to represent the derivative of the parabola function in three different ™ positions.
Example 1: Find the derivative of ,‡,™.=θ™+ -Υ.
Example 2: Compute the derivative of ‡,™.=Υ,™-β.−φ™ at ™=θ:
Example 3: Find the equation of the line tangent to the graph of ‡,™.=,Ϗ-™. at ™=β
Example 4: Find the derivative of ‡,™.=,™.
Example 6: Graph the function ‡,™.=,™-θ.−Υ™ , and its derivative ,‡-′.,™.=θ,™-β.−Υ.
Solve by yourself using the definition of the derivative.
Them, use Wolfram Alpha to interpreter the answer.
To succeed in this topic, you should understand
Homework Topic 2.1
PROJECT-2. The Derivative Using Limit Definition
Example 2. Compute the derivative of ‡,™.=Υ,™-β.−φ™ at ™=θ:
Example 3. Find the equation of the line tangent to the graph of ‡,™.=,Ϗ-™. at ™=β
Complete the following exercises using limit definition
2.2. Techniques of differentiation.
2.3. Product and Quotient Rules
Example (product rule) 1
Example (quotient rule) 2:
Homework Topic 2.2 and 2.3.
2.4. The Chain Rule
Definition of the Chain Rule or differentiation of a composite function:
Example 1: Given: ,‰,™.=-,,(™-β.−Ύ™+Ύ)-θ.., find ,‰-′.,™..
Example 2: š=,™+,†-™..
Example 3: š=,,Ϗ−θ™.-θ.,,β,™-β.+θ.-Ύ.
Example 4: š=,™-β.(,%'-(,™-β.)).
2.5. Implicit Differentiation.
2.6. High Order Derivatives (second, third, ...):
Homework Topics 2.4, 2.5, and 2.6.
PRACTICING QUIZ-2. Derivatives
2.7. Real Case Examples (Marginal Analysis and Approximations)
To succeed in these topics, you should understand
Homework Topic 2.7.
2.8. Increasing and Decreasing Functions (critical points)
To succeed in these topics, you should understand
2.9. Rolle's Theorem and The Mean Value Theorem
Proof:
Example: 1
Example 2.
Homework Topic 2.8 and 2.9.
2.10. Concavity and Point of Inflexion
Sufficient condition of concavity (convexity) of a function:
Homework Topic 2.10.
PRACTICING QUIZ-3. Application of Derivatives
CHAPTER-3. EXPONENTIAL and LOGARITHMIC FUNCTIONS. OPTIMIZATIONS.
3.1. Remembering Exponential and Logarithmic Functions (an Algebra Topic):
3.1.2. Exponential Functions.
3.1.3. Logarithmic Functions.
Examples:
3.1.4. Properties of Logarithms:
3.1.5. Exponential and Logarithmic Equations
3.1.6. Compound Interest. Periodic and Continuous Compounding Interest:
Homework Topic 3.1
Exponential Functions.
Logarithmic Functions and Properties of Logarithms.
Exponential and Logarithmic Equations.
Compound Interest.
Additional Homework Topic 3.1.5-plus:
Exponential Growth and Decay exercises:
3.2. Differentiation of Exponential Functions
3.3. Differentiation of Logarithmic Functions
Homework Topic 3.2 and 3.3
Differentiate given expression
In exercises from 198 to 201 find an equation for the tangent line to š=‡,™.at the specified point:
3.4. L’ Hospital Rule / Revisiting Limits
How L’Hôpital’s Rule works?
Homework Topic 3.4.
3.5. Optimization and Business Applications Examples.
3.5.1. Application to Volume optimization
3.5.2. Application to Analytic Geometry:
3.5.3. Application to evacuation situation.
3.5.4. Application in Electrical Engineering:
3.5.5. More about Related Rate of Change in time.
Homework Topic 3.5.
PRACTICING QUIZ-4. Optimization, Exponential and Logarithmic Functions.
PROJECT-3. Quick Example of a Business Profit Optimization
I. General Information:
II. Specific Information/Data:
III. Analysis
IV. Conclusion
CHAPTER-4. INTEGRATION
4.1. Indefinite Integration and Simple Differential Equation
The General Power Rule for Integration (indefinite integral) and other rules for common functions:
4.2. Integration by substitution
Homework Topic 4.1 and 4.2.
Find the indicated integral. Apply substitution method.
4.3. Riemann Integration / Riemann Sum.
Homework Topic 4.3
4.4. Fundamental Theorem of Calculus and Definite Integral
Properties of Definite Integral
4.5. Application of Integrals (Average Function Value).
Homework Topic 4.4 and 4.5.
4.6. Application of Integrals (Area Under and Between Curves).
The definite integral can be used to find the area between a graph curve and the ‘e’ axis, between two given e values. This area is called the ‘area under the curve’ regardless of whether it is above or below the ‘e’ axis.
To succeed in this topic, you should understand
Homework Topic 4.6
PRACTICING QUIZ-5. Integrals and its applications
PROJECT – 4. Optimization of the Material Cost.
The Problem:
Analysis
First Conclusion:
Now let us work with the legs:
PROJECT – 5. Profit Optimization (Transport Marine Company)
PROJECT – 6. Optimization of fictitious city evacuation.
CHAPTER 5. INTRODUCTORY STATISTICS WITH CALCULUS.
5.1. Continuous Random Variable, Probability, and Histograms.
5.2. Probability Density Functions: Uniform, Exponential, and Normal.
5.3. Uniform Density Function
5.4. Exponential Density Functions
5.5. Normal Distribution
5.6. Mean and Median.
5.7. Variance and Standard Deviation
Now Let’s review some statistical properties of variance and deviation:
5.8. Variance in different types of distributions:
1. Case Study Uniform Distribution
2. Case Study Exponential Distribution
3. Case Study Normal Distribution
Homework Chapter 5
Homework and practicing exercises at Prieto-Valdes web-page
PROJECT – 7. Portfolio Optimization
Application of previously developed template:
REVIEW CHAPTER.
R-1. Some Elementary Algebra Concepts
R-1.1. Common Factors
R-1.2. Exponents
R-1.3. Roots; Products, Addition, and Subtraction Rules for Square Roots
R-1.4. Rationalizing the Denominators
R-1.5. Polynomials, Addition/Subtraction, Multiplication, Special Products, and Factoring
R-1.6. The Product of Two Binomials (Foil Method)
R-1.7. Special Product Rules
R-1.8. Greatest Common Factor (GCF) and Factoring by Grouping
R-1.9. Factoring Trinomials in the Form ,™-β.+ƒ™+„ and ,‚™-β.+ƒ™+„ where ‚≠Ϗ
R-1.10. Rational Expressions, Multiplication and Division:
R-1.11. Addition/subtraction. Finding the Low Common Denominator (LCD)
R-1.12. Compound Rational Expressions
R-2. Algebra Review
R-2.1. Lines, Slope, and Graphing Linear Functions.
R-2.2. Solving Linear Equations
R.2.3. Rational Equations
R-2.4. Complex Numbers.
Complex numbers are combination of real and imaginary number parts:
R-2.5. Quadratic Equation.
R-2.6. Radical Equations.
R-2.7. Other Types of Equations
R-2.8. Absolute Value Equations & Inequalities.
R.2.9. Factoring Before Calculus.
R-2.11. Functions and Their Graph.
R-2.12 Graphing Technics and Transformation of Functions.
R-2.13. General Characteristics of Functions
R-3.14. Combination and Composition of Functions.
R-2.15. Quadratic Functions.
The relation ,™-—.=−,ƒ-β‚. also can be obtained using the middle point between zero solutions,™-Ϗ,β.:
Example: When no intercepts with axis X (left) and with interception (right)
R-2.16. Elementary Properties and Graph of Polynomial Functions.
End Behavior
Continuous and discontinuous function:
Multiplicity, an important attribute of the polynomial functions:
Number of solutions and turning points on the graph
Examples:
R-2.17. The Real Zeros of a Polynomial.
FACTOR THEOREM:
Proof:
Equivalencies:
Example:
Examples using ,‚-.=Ϗ. In this case ‘ is a possible factor of ,‚-ώ., then ‘ is a solution.
Examples:
Model Example: Finding the zeroes of a polynomial.
R-2.18. Complex Zeros and the Fundamental Theorem of Algebra
Steps for Finding the Real Zeros of a Polynomial Function. When graphing a Polynomial Function is convenient to follow the following steps:
R-2.19. Property and Graph of Rational Functions.
Descriptive examples:
R-2.21. Polynomial and Rational Inequalities

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