Limits and Continuity
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Starting Limits (10:30)
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Evaluating Limits Graphically (11:37)
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Evaluating Limits Numerically (9:33)
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Limits that Don’t Exist (12:02)
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One Sided and Two Sided Limits (14:58)
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Properties of Limits (11:40)
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Formal Definition of a Limit (14:20)
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Evaluating Limits Directly (13:58)
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Functions That Agree at All But One Point (9:09)
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Evaluating Limits Algebraically (14:22)
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The Squeeze Theorem (10:04)
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Starting Continuity (7:49)
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Formal Definition of Continuity (17:35)
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Continuity on a Closed Interval (13:29)
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Properties of Continuity (11:55)
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The Intermediate Value Theorem (13:15)
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Practice Questions
The Derivative
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Average and Instantaneous Rate of Change (15:04)
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The Limit Definition of the Slope of a Tangent Line (14:17)
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Defining The Derivative (14:47)
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Differentiability (15:17)
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Derivative Notation (8:33)
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The Power Rule (15:09)
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The Product Rule (14:48)
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The Quotient Rule (12:54)
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Differentiating Trigonometric Functions (10:25)
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Practice Questions
The Chain Rule & Advanced Techniques
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The Chain Rule (33:51)
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Implicit Differentiation (17:28)
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Second Derivates (11:23)
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Combining Differentiation Rules (15:52)
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Differentiating Exponential Functions (14:33)
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Differentiating Logarithmic Functions (10:57)
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Differentiating Inverse Functions (9:07)
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Differentiating Inverse Trigonometric Functions (9:22)
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L’Hopitals Rule (13:08)
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Practice Questions
Applications of Derivatives
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The Equation of a Tangent to a Curve (14:37)
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Determining Whether a Function is Increasing or Decreasing (18:50)
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Determining Local Extrema of a Function (15:20)
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2nd Derivative Test (15:50)
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Points of Inflection (14:38)
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Concavity (26:09)
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Determining the Nature of Stationary Points (16:28)
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Sketching Curves (18:56)
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Optimization Problems (27:52)
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Rolle’s Theorem (13:26)
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The Mean Value Theorem (15:15)
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Practice Questions
Additional Resources
