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Graphs and Limits
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Classroom Contents
Calculus 1
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- 1 Graphs and Limits
- 2 When Limits Fail to Exist
- 3 Limit Laws
- 4 The Squeeze Theorem
- 5 Limits using Algebraic Tricks
- 6 When the Limit of the Denominator is 0
- 7 Limits at Infinity and Graphs
- 8 Limits at Infinity and Algebraic Tricks
- 9 Continuity at a Point
- 10 Continuity Example with a Piecewise Defined Function
- 11 Continuity on Intervals
- 12 Continuity and Domains
- 13 Intermediate Value Theorem
- 14 Derivatives and Tangent Lines
- 15 Computing Derivatives from the Definition
- 16 Interpreting Derivatives
- 17 Derivatives as Functions and Graphs of Derivatives
- 18 Proof that Differentiable Functions are Continuous
- 19 Power Rule and Other Rules for Derivatives
- 20 Higher Order Derivatives and Notation
- 21 Derivative of e^x
- 22 Proof of the Power Rule and Other Derivative Rules
- 23 Product Rule and Quotient Rule
- 24 Proof of Product Rule and Quotient Rule
- 25 Special Trigonometric Limits
- 26 Derivatives of Trig Functions
- 27 Proof of Trigonometric Limits and Derivatives
- 28 Derivatives and Rates of Change (Rectilinear Motion)
- 29 Marginal Cost
- 30 The Chain Rule
- 31 More Chain Rule Examples and Justification
- 32 Justification of the Chain Rule
- 33 Implicit Differentiation
- 34 Derivatives of Exponential Functions
- 35 Derivatives of Log Functions
- 36 Logarithmic Differentiation
- 37 Inverse Trig Functions
- 38 Derivatives of Inverse Trigonometric Functions
- 39 Related Rates - Distances
- 40 Related Rates - Volume and Flow
- 41 Related Rates - Angle and Rotation
- 42 Maximums and Minimums
- 43 Mean Value Theorem
- 44 Proof of Mean Value Theorem
- 45 Derivatives and the Shape of the Graph
- 46 First Derivative Test and Second Derivative Test
- 47 Derivatives and the shape of the graph - example
- 48 Extreme Value Examples
- 49 Linear Approximation
- 50 The Differential
- 51 L'Hospital's Rule
- 52 L'Hospital's Rule on Other Indeterminate Forms
- 53 Newtons Method
- 54 Antiderivatives
- 55 Finding Antiderivatives Using Initial Conditions
- 56 Any Two Antiderivatives Differ by a Constant
- 57 Summation Notation
- 58 Approximating Area
- 59 The Fundamental Theorem of Calculus, Part 1
- 60 The Fundamental Theorem of Calculus, Part 2
- 61 Proof of the Fundamental Theorem of Calculus
- 62 The Substitution Method
- 63 Why U-Substitution Works
- 64 Average Value of a Function
- 65 Proof of the Mean Value Theorem for Integrals
- 66 Recitation 2 a solution and some hints
- 67 Limit as x goes to infinity recitation problem
