Business Calculus One

Introduction: What is a limit?

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Stars at Night

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Geometric View of Limits

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Geometric View - One Sided Limits

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Analytic View - Tables

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Limits: Notation, One-sided Limits, and Formal Definitions

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Limit laws

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Equal or not?

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The limit laws

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Continuity and the Intermediate Value Theorem

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Roxy and Yuri like food

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Continuity

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Left/Right Continuity

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Continuity and Limit Laws

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Continuity of piecewise functions

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The Intermediate Value Theorem

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(In)determinate forms

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Could it be anything?

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Limits at Infinity

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What Are Indeterminate Forms?

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Limits of the form zero over zero

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Limits of the form nonzero over zero

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Using limits to detect asymptotes

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Zoom out

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Vertical asymptotes

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Horizontal asymptotes

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An application of limits

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Limits and velocity

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Instantaneous velocity

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Introduction

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Overview

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Derivatives: Geometric View

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Derivatives: Analytic View

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Derivative Conditions

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Derivative Functions

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Derivative And Continuity

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Decomposing Derivatives

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Sum/Difference Rule

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Polynomial Rule

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Product Rule

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Quotient Rule

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Chain Rule

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When/How to Multi Chain Rule

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Implicit Differentiation

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Remaining Functions

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Exponential Functions

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Logarithmic Functions

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Supplemental Techniques

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Logarithmic Differentiation

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Finding Extrema

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Local Extrema

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Extreme Value Theorem

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Absolute Extrema

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Concavity

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Geometric View

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Analytic View

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Points of Inflection Geometric View

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Points of Inflection Analytic View

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Second Derivative Test

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Practical Applications

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Newtonian Mechanics

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Graphing Functions

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Geometric View of Linear Approximation

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Analytic View of Linear Approximation

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Related Rates

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Optimization

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Introduction

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Sigma Notation

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Antiderivative Intro

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Antiderivatives of Core Functions

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Riemann Approximations

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Area under the Curve

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Riemann Approximation Types

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The Definite Integral!

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Perfect Approximations!

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Condensing the Notation, the Indefinite Integral!

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The Indefinite Integral!

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Indefinite Integral

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Classes of Functions

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Fundamental Theorem of Calculus

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First Theorem

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Second Theorem

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U-Substitution

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U-Substitution

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How to see a U-Sub

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Overall

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