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Calculus 5.4.1 The Natural Exponential Function
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Classroom Contents
Calculus I - Entire Course
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- 1 Calculus 1.1 A Preview of Calculus
- 2 Calculus 1.2.1 Find Limits Graphically and Numerically: Estimate a Limit Numerically or Graphically
- 3 Calculus 1.2.2 Find Limits Graphically and Numerically: When Limits Fail to Exist
- 4 Calculus 1.2.3 Find Limits Graphically and Numerically: The Formal Definition of A Limit
- 5 Calculus 1.3.1 Evaluating Limits Using Properties of Limits
- 6 Calculus 1.3.2 Evaluating Limits By Dividing Out or Rationalizing
- 7 Calculus 1.3.3 Evaluating Limits Using the Squeeze Theorem
- 8 Calculus 1.4.1 Continuity on Open Intervals
- 9 Calculus 1.4.2 Continuity on Closed Intervals
- 10 Calculus 1.4.3 Properties of Continuity
- 11 Calculus 1.4.4 The Intermediate Value Theorem
- 12 Calculus 1.5.1 Determine Infinite Limits
- 13 Calculus 1.5.2 Determine Vertical Asymptotes
- 14 Calculus 2.1.1 Find the Slope of a Tangent Line
- 15 Calculus 2.1.2 Derivatives Using the Limit Definition
- 16 Calculus 2.1.3 Differentiability and Continuity
- 17 Calculus 2.2.1 Basic Differentiation Rules
- 18 Calculus 2.2.2 Rates of Change
- 19 Calculus 2.3.1 The Product and Quotient Rules
- 20 Calculus 2.3.2 Derivatives of Trigonometric Functions
- 21 Calculus 2.3.3 Higher Order Derivatives
- 22 Calculus 2.4.1 The Chain Rule
- 23 Calculus 2.4.2 The General Power Rule
- 24 Calculus 2.4.3 Simplifying Derivatives
- 25 Calculus 2.4.4 Trigonometric Functions and the Chain Rule
- 26 Calculus 2.5.1 Implicit and Explicit Functions
- 27 Calculus 2.5.2 Implicit Differentiation
- 28 Calculus I - 2.6.1 Related Rates - Water Ripples (2D Circle)
- 29 Calculus I - 2.6.2 Related Rates - Balloon Inflation (Sphere)
- 30 Calculus I - 2.6.3 Related Rates - Modeling with Triangles
- 31 Calculus 3.1.1 Extrema of a Function on an Interval
- 32 Calculus 3.1.2 Relative Extrema of a Function on an Open Interval
- 33 Calculus 3.1.3 Find Extrema on a Closed Interval
- 34 Calculus 3.2.1 Rolle’s Theorem
- 35 Calculus 3.2.2 The Mean Value Theorem
- 36 Calculus 3.3.1 Increasing and Decreasing Intervals
- 37 Calculus 3.3.2 The First Derivative Test
- 38 Calculus 3.4.1 Intervals of Concavity
- 39 Calculus 3.4.2 Points of Inflection
- 40 Calculus 3.4.3 The Second Derivative Test
- 41 Calculus 3.4.4 Putting It All Together
- 42 Calculus 3.5.1 Determine Finite Limits at Infinity
- 43 Calculus 3.5.2 Determine Horizontal Asymptotes of a Function
- 44 Calculus 3.5.3 Horizontal Asymptotes - Tricky Examples
- 45 Calculus 3.5.4 Determine Infinite Limits at Infinity
- 46 Calculus 3.6.1 A Summary of Curve Sketching
- 47 Calculus 3.6.2 Curve Sketching - Full Practice
- 48 Calculus 3.7.1 Optimization Problems
- 49 Calculus 3.7.2 Optimization Practice
- 50 Calculus 4.1.1 Antiderivatives
- 51 Calculus 4.1.2 Basic Integration Rules
- 52 Calculus 4.1.3 Find Particular Solutions to Differential Equations
- 53 Calculus 4.2.1 Sigma Notation
- 54 Calculus 4.2.2 The Concept of Area
- 55 Calculus 4.2.3 The Approximate Area of a Plane Region
- 56 Calculus 4.2.4 Finding Area By The Limit Definition
- 57 Calculus 4.3.1 Riemann Sums
- 58 Calculus 4.3.2 Definite Integrals
- 59 Calculus 4.3.3 Properties of Definite Integrals
- 60 Calculus 4.4.1 The Fundamental Theorem of Calculus
- 61 Calculus 4.4.2 The Mean Value Theorem for Integrals
- 62 Calculus 4.4.3 The Average Value of a Function
- 63 Calculus 4.4.4 The Second Fundamental Theorem of Calculus
- 64 Calculus 4.5.1 Use Pattern Recognition in Indefinite Integrals
- 65 Calculus 4.5.2 Change of Variables for Indefinite Integrals
- 66 Calculus 5.1.1 Properties of the Natural Logarithmic Function
- 67 Calculus 5.1.2 The Number e
- 68 Calculus 5.1.3 The Derivative of the Natural Logarithmic Function
- 69 Calculus 5.2.1 The Log Rule for Integration
- 70 Calculus 5.2.2 Integrals of Trigonometric Functions
- 71 Calculus 5.3.1 Verify Functions are Inverses of One Another
- 72 Calculus 5.3.2 Determine Whether a Function Has An Inverse
- 73 Calculus 5.3.3 Find the Inverse of a Function
- 74 Calculus 5.3.4 Find the Derivative of an Inverse of a Function
- 75 Calculus 5.4.1 The Natural Exponential Function
- 76 Calculus 5.4.2 Derivatives of the Natural Exponential Function
- 77 Calculus 5.4.3 Integrals of the Natural Exponential Function
- 78 Calculus 5.5.1 Exponential Functions with Bases Other than e
- 79 Calculus 5.5.2 Differentiate and Integrate with Bases Other than e
- 80 Calculus 5.5.3 Applications of Bases Other than e
- 81 Calculus 5.6.1 Indeterminate Forms
- 82 Calculus 5.6.2 L’Hôpital’s Rule
- 83 Calculus 5.7.1 Inverse Trigonometric Functions
- 84 Calculus 5.7.2 Derivatives of Inverse Trigonometric Functions
- 85 Calculus 5.8.1 Integrate Inverse Trigonometric Functions
- 86 Calculus 5.8.2 Integrate Using the Completing the Square Technique
