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- Precalculus & Elements of Calculus
- Chapter 0
- Chapter 1
- Chapter 2
- Chapter 3
Chapter 3.1: Slope of a Curve
- 01) Introduction
- 02) Intro. (Cont’d) and Average Rate of Change
- 03) Average Rate of Change (Cont’d)
- 04) Ave. and Instantaneous Rate of Change
- 05) Approximating Instantaneous Rate of Change, Part I
- 06) Approximating Instantaneous Rate of Change, Part II
- 07) Approximating Instantaneous Rate of Change, Part III
- 08) Introduction to Slope of Curve/Tangent Line
- 09) Slope of Secant Approximating Slope of Tangent
- 10) The Slope as a Limit
- 11) Finding Slope of Tangent to a Curve at a Point
- 12) Finding Slope to Curve (Cont’d)
- 13) Finding Slope of Tangent, Example 2
- 14) Finding Slope of Curve at 4 Different Points
- 15) Slope at 4 Different Points (Cont’d)
- 16) Intro to Using Calculator
- 17) Calculator Tips-Slope of Tangent Line
- 18) Equation of Tangent Line Part I
- 19) Equation of Tangent Line, Part II
- 20) Equation of Tangent Line, Part III
- 21) Equation of Tangent Line, Part IV
- 22) Introduction to Slope of Square Root Functions
- 23) Finding Slopes of Square Root Functions, Part I
- 24) Calculator Investigation of Square Root Problem
- 25) Finding Slopes of Square Root Functions, Part II
- 26) Finding Equation of Tangent Line to Square Root Function
- 27) Slope of Square Root Function, Example 2
- 28) Slope of Square Root Function at Any x
- 29) Existence of Tangent Line, Part I
- 30) Existence of Tangent Line, Part II
- 31) Existence of Tangent Line, Part III
- 32) Slope of a Piecewise-Defined Function
- 33) The Derivative and its Notation, Part I
- 34) Derivative Notation, Part II
- 35) Derivative of Cubic Function, Part I
- 36) Derivative of Cubic Function, Part II
- 37) Calculator Tip for Homework Problems
Chapter 3.2: Derivative Rules I
- 01) Introduction-Derivative of xn
- 02) Derivatives of Linear and Constant Functions of Derivative of xn, Part I
- 03) Proof of Derivative of xn, Part II
- 04) Review of Laws of Exponents, Part I
- 05) Review of Laws of Exponents, Part II
- 06) Constant Multiplier Rule and Examples
- 07) The Sum Rule and Examples
- 08) Derivative of a Polynomial
- 09) Equation of Tangent Line
- 10) Equation Tangent Line and Error
- 11) Understanding Percent Error
- 12) Calculators Tips
Chapter 3.3: Limits and Continuity
- 01) Intro. to Limits, Part I
- 02) Intro. to Limits, Part II
- 03) Intro. to Limits, Part III
- 04) Intro. to Limits, Part IV
- 05) Intro. to Limits, Part V
- 06) Intro. to Limits, Part VI
- 07) Limit Example 1
- 08) Limit Example 2
- 09) Limit Example 3
- 10) Limit Practice Problem
- 11) Theorem 1: Limit of Constant
- 12) Thm 2: Limit of x
- 13) Thm 3: Limit of kf(x)
- 14) Thm 4: Limit of f(x) + g(x)
- 15) Thm 5: Limit of f(x)g(x)
- 16) Thm 6: Limit of f(x)/g(x)
- 17) Thm 7: Limit of [f(x)]^N
- 18) Limit of Square Root
- 19) Limits Using Theorems
- 20) Limit of Difference Quotient
- 21) Another Difference Quotient Limit
- 22) One-Sided Limits
- 23) Limits of Piecewise Defined Functions
- 24) Piecewise Defined with "Hole"
- 25) Piecewise Defined with "Jump"
- 26) Piecewise Limit without Graph
- 27) Practice with Piecewise
- 28) Continuity, Part I
- 29) Continuity, Part II
- 30) Continuity, Part III
- 31) Definition of Continuous
- 32) Example: "Discuss Continuity"
- 33) Differentiability and Continuity
Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes
- 01) Why Division by 0 is Undefined and 0/0 Indeterminate
- 02) Lim as x->0+ of 1/x
- 03) Lim as x->0- of 1/x
- 04) Lim as x->0 of 1/x
- 05) Lim as x->0 of 1/x2
- 06) Lim as x->0 of -1/x2 and Shortcut to Finding Infinite Limits
- 07) Lim as x->2 of 1/(x-2)
- 08) 4 Examples of Infinite Limits
- 09) Lim as x->a+ of 1/(x-a)n
- 10) Lim as x->a- of 1/(x-a)n and lim x->-3- of x/(x+3)
- 11) Lim as x->-3+ of x/(x+3)
- 12) Lim as x->-7-
- 13) 2 More Infinite Limits
- 14) Pond Problem 1
- 15) Pond Problem 2
- 16) Pond Problem 3
- 17) Lim as x->infinity of (100,000 + 215x) / x
- 18) Shortcuts for 2 Limits at Infinity
- 19) 3 Limits x-> Infinity
- 20) More Limits at Infinity, and Summary
- 21) Sketch Graph of Rational Function
- 22) TI-89: Finding Limits
- 23) TI-89: Finding Limits at Infinity and Infinite Limits Exactly
- 24) A Problem Similar to Homework, Part I
- 25) A Problem from Homework, Part II
- 26) Another Homework Problem
Chapter 3.5: Derivative Rules 2
- 01) Summary of Derivative Rules
- 02) Motivating Product Rule
- 03) Product Rule Example 1
- 04) Product Rule Example 2
- 05) Product Rule Example 3
- 06) Product Rule with Square Root
- 07) Motivating Quotient Rule
- 08) Another Quotient to Differentiate
- 09) Quotient Rule Example 1
- 10) Quotient Rule Example 2
- 11) Quotient Rule Example 3
- 12) Using TI-89 to Show Equivalent Expressions
Chapter 3.6: The Chain Rule
- 01) Review/Derivative of Composite Function
- 02) Motivating the Chain Rule
- 03) Chain Rule
- 04) Chain Rule Example
- 05) Chain Rule Example 2
- 06) Chain Rule Example 3
- 07) General Power Rule
- 08) Equation of Tangent Line
- 09) Derivative of Square Root with Chain Rule
- 10) Product and Chain Rules Together
- 11) Chain, then Quotient Rule
- 12) Quotient, then Chain Rule
- 13) Another Use for Chain Rule, Part I
- 14) Another Use for Chain Rule, Part II
Chapter 3.7: Marginal Funcations and Rates of Change
- 01) Marginal Cost, Example 1
- 02) Marginal Cost, Example 2
- 03) Practice Finding Marginal Cost
- 04) Definition of Marginals
- 05) Intro to Derivative
- 06) Summary of Marginal vs. Derivative
- 07) E'(x) approximates E(x+1) - E(x)
- 08) Practice: Change in Revenue
- 09) Percent Error of Approximation
- 10) Average Cost, Revenue, or Profit
- 11) TI-89 and Average Rate of Change
- 12) Vertical Motion, Part I
- 13) Vertical Motion, Part II
- 14) Vertical Motion, Part III
- 15) Average vs. Instantaneous Velocity
- 16) Why Derivative Gives Instant. ROC
- 17) Problems Using ROC, Part I
- 18) Problems Using ROC, Part II
- 19) Practice with Instant. Vel.
Chapter 3.8: Implicit Differentiation
- 01) Intro. to Implicit Differentiation
- 02) Slope of a Circle, Part I
- 03) Slope of a Circle using Imp. Diff.
- 04) Equation of Tangent to Circle
- 05) Practice: Equation Tangent Line
- 06) Imp. Diff. Example 4
- 07) Imp. Diff. Example 5
- 08) Imp. Diff. Example 6
- 09) Imp. Diff. Example 7
- 10) Imp. Diff. Example 8
- 11) TI-89 and Implicit Differentiation
Chapter 3.10: Related Rates
- 01) Related Rates: Shuttle Launch
- 02) Shuttle Launch, Part II
- 03) Oil Spill
- 04) Shadows and Similar Triangles
Chapter 3.11: Newton's Method
- 01) Newton's Method
- 02) Newton's Method on Excel
- 03) Newton's Method on TI-89
Chapter 3
Chapter 3.1: Slope of a Curve
- 01) Introduction
- 02) Intro. (Cont’d) and Average Rate of Change
- 03) Average Rate of Change (Cont’d)
- 04) Ave. and Instantaneous Rate of Change
- 05) Approximating Instantaneous Rate of Change, Part I
- 06) Approximating Instantaneous Rate of Change, Part II
- 07) Approximating Instantaneous Rate of Change, Part III
- 08) Introduction to Slope of Curve/Tangent Line
- 09) Slope of Secant Approximating Slope of Tangent
- 10) The Slope as a Limit
- 11) Finding Slope of Tangent to a Curve at a Point
- 12) Finding Slope to Curve (Cont’d)
- 13) Finding Slope of Tangent, Example 2
- 14) Finding Slope of Curve at 4 Different Points
- 15) Slope at 4 Different Points (Cont’d)
- 16) Intro to Using Calculator
- 17) Calculator Tips-Slope of Tangent Line
- 18) Equation of Tangent Line Part I
- 19) Equation of Tangent Line, Part II
- 20) Equation of Tangent Line, Part III
- 21) Equation of Tangent Line, Part IV
- 22) Introduction to Slope of Square Root Functions
- 23) Finding Slopes of Square Root Functions, Part I
- 24) Calculator Investigation of Square Root Problem
- 25) Finding Slopes of Square Root Functions, Part II
- 26) Finding Equation of Tangent Line to Square Root Function
- 27) Slope of Square Root Function, Example 2
- 28) Slope of Square Root Function at Any x
- 29) Existence of Tangent Line, Part I
- 30) Existence of Tangent Line, Part II
- 31) Existence of Tangent Line, Part III
- 32) Slope of a Piecewise-Defined Function
- 33) The Derivative and its Notation, Part I
- 34) Derivative Notation, Part II
- 35) Derivative of Cubic Function, Part I
- 36) Derivative of Cubic Function, Part II
- 37) Calculator Tip for Homework Problems
Chapter 3.2: Derivative Rules I
- 01) Introduction-Derivative of xn
- 02) Derivatives of Linear and Constant Functions of Derivative of xn, Part I
- 03) Proof of Derivative of xn, Part II
- 04) Review of Laws of Exponents, Part I
- 05) Review of Laws of Exponents, Part II
- 06) Constant Multiplier Rule and Examples
- 07) The Sum Rule and Examples
- 08) Derivative of a Polynomial
- 09) Equation of Tangent Line
- 10) Equation Tangent Line and Error
- 11) Understanding Percent Error
- 12) Calculators Tips
Chapter 3.3: Limits and Continuity
- 01) Intro. to Limits, Part I
- 02) Intro. to Limits, Part II
- 03) Intro. to Limits, Part III
- 04) Intro. to Limits, Part IV
- 05) Intro. to Limits, Part V
- 06) Intro. to Limits, Part VI
- 07) Limit Example 1
- 08) Limit Example 2
- 09) Limit Example 3
- 10) Limit Practice Problem
- 11) Theorem 1: Limit of Constant
- 12) Thm 2: Limit of x
- 13) Thm 3: Limit of kf(x)
- 14) Thm 4: Limit of f(x) + g(x)
- 15) Thm 5: Limit of f(x)g(x)
- 16) Thm 6: Limit of f(x)/g(x)
- 17) Thm 7: Limit of [f(x)]^N
- 18) Limit of Square Root
- 19) Limits Using Theorems
- 20) Limit of Difference Quotient
- 21) Another Difference Quotient Limit
- 22) One-Sided Limits
- 23) Limits of Piecewise Defined Functions
- 24) Piecewise Defined with "Hole"
- 25) Piecewise Defined with "Jump"
- 26) Piecewise Limit without Graph
- 27) Practice with Piecewise
- 28) Continuity, Part I
- 29) Continuity, Part II
- 30) Continuity, Part III
- 31) Definition of Continuous
- 32) Example: "Discuss Continuity"
- 33) Differentiability and Continuity
Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes
- 01) Why Division by 0 is Undefined and 0/0 Indeterminate
- 02) Lim as x->0+ of 1/x
- 03) Lim as x->0- of 1/x
- 04) Lim as x->0 of 1/x
- 05) Lim as x->0 of 1/x2
- 06) Lim as x->0 of -1/x2 and Shortcut to Finding Infinite Limits
- 07) Lim as x->2 of 1/(x-2)
- 08) 4 Examples of Infinite Limits
- 09) Lim as x->a+ of 1/(x-a)n
- 10) Lim as x->a- of 1/(x-a)n and lim x->-3- of x/(x+3)
- 11) Lim as x->-3+ of x/(x+3)
- 12) Lim as x->-7-
- 13) 2 More Infinite Limits
- 14) Pond Problem 1
- 15) Pond Problem 2
- 16) Pond Problem 3
- 17) Lim as x->infinity of (100,000 + 215x) / x
- 18) Shortcuts for 2 Limits at Infinity
- 19) 3 Limits x-> Infinity
- 20) More Limits at Infinity, and Summary
- 21) Sketch Graph of Rational Function
- 22) TI-89: Finding Limits
- 23) TI-89: Finding Limits at Infinity and Infinite Limits Exactly
- 24) A Problem Similar to Homework, Part I
- 25) A Problem from Homework, Part II
- 26) Another Homework Problem
Chapter 3.5: Derivative Rules 2
- 01) Summary of Derivative Rules
- 02) Motivating Product Rule
- 03) Product Rule Example 1
- 04) Product Rule Example 2
- 05) Product Rule Example 3
- 06) Product Rule with Square Root
- 07) Motivating Quotient Rule
- 08) Another Quotient to Differentiate
- 09) Quotient Rule Example 1
- 10) Quotient Rule Example 2
- 11) Quotient Rule Example 3
- 12) Using TI-89 to Show Equivalent Expressions
Chapter 3.6: The Chain Rule
- 01) Review/Derivative of Composite Function
- 02) Motivating the Chain Rule
- 03) Chain Rule
- 04) Chain Rule Example
- 05) Chain Rule Example 2
- 06) Chain Rule Example 3
- 07) General Power Rule
- 08) Equation of Tangent Line
- 09) Derivative of Square Root with Chain Rule
- 10) Product and Chain Rules Together
- 11) Chain, then Quotient Rule
- 12) Quotient, then Chain Rule
- 13) Another Use for Chain Rule, Part I
- 14) Another Use for Chain Rule, Part II
Chapter 3.7: Marginal Funcations and Rates of Change
- 01) Marginal Cost, Example 1
- 02) Marginal Cost, Example 2
- 03) Practice Finding Marginal Cost
- 04) Definition of Marginals
- 05) Intro to Derivative
- 06) Summary of Marginal vs. Derivative
- 07) E'(x) approximates E(x+1) - E(x)
- 08) Practice: Change in Revenue
- 09) Percent Error of Approximation
- 10) Average Cost, Revenue, or Profit
- 11) TI-89 and Average Rate of Change
- 12) Vertical Motion, Part I
- 13) Vertical Motion, Part II
- 14) Vertical Motion, Part III
- 15) Average vs. Instantaneous Velocity
- 16) Why Derivative Gives Instant. ROC
- 17) Problems Using ROC, Part I
- 18) Problems Using ROC, Part II
- 19) Practice with Instant. Vel.
Chapter 3.8: Implicit Differentiation
- 01) Intro. to Implicit Differentiation
- 02) Slope of a Circle, Part I
- 03) Slope of a Circle using Imp. Diff.
- 04) Equation of Tangent to Circle
- 05) Practice: Equation Tangent Line
- 06) Imp. Diff. Example 4
- 07) Imp. Diff. Example 5
- 08) Imp. Diff. Example 6
- 09) Imp. Diff. Example 7
- 10) Imp. Diff. Example 8
- 11) TI-89 and Implicit Differentiation
Chapter 3.10: Related Rates
- 01) Related Rates: Shuttle Launch
- 02) Shuttle Launch, Part II
- 03) Oil Spill
- 04) Shadows and Similar Triangles
Chapter 3.11: Newton's Method
- 01) Newton's Method
- 02) Newton's Method on Excel
- 03) Newton's Method on TI-89
