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Linear Approximations | Using Tangent Lines to Approximate Functions
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Classroom Contents
Calculus I - Limits, Derivative, Integrals
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- 1 The Velocity Problem | Part I: Numerically
- 2 The Velocity Problem | Part II: Graphically
- 3 A Tale of Three Functions | Intro to Limits Part I
- 4 A Tale of Three Functions | Intro to Limits Part II
- 5 What is an infinite limit?
- 6 Limit Laws | Breaking Up Complicated Limits Into Simpler Ones
- 7 Building up to computing limits of rational functions
- 8 Limits of Oscillating Functions and the Squeeze Theorem
- 9 Top 4 Algebraic Tricks for Computing Limits
- 10 A Limit Example Combining Multiple Algebraic Tricks
- 11 Limits are simple for continuous functions
- 12 Were you ever exactly 3 feet tall? The Intermediate Value Theorem
- 13 Example: When is a Piecewise Function Continuous?
- 14 Limits "at" infinity
- 15 Computing Limits at Infinity for Rational Functions
- 16 Infinite Limit vs Limits at Infinity of a Composite Function
- 17 How to watch math videos
- 18 Definition of the Derivative | Part I
- 19 Applying the Definition of the Derivative to 1/x
- 20 Definition of Derivative Example: f(x) = x + 1/(x+1)
- 21 The derivative of a constant and of x^2 from the definition
- 22 Derivative Rules: Power Rule, Additivity, and Scalar Multiplication
- 23 How to Find the Equation of a Tangent Line
- 24 The derivative of e^x.
- 25 The product and quotient rules
- 26 The derivative of Trigonometric Functions
- 27 Chain Rule: the Derivative of a Composition
- 28 Interpreting the Chain Rule Graphically
- 29 The Chain Rule using Leibniz notation
- 30 Implicit Differentiation | Differentiation when you only have an equation, not an explicit function
- 31 Derivative of Inverse Trig Functions via Implicit Differentiation
- 32 The Derivative of ln(x) via Implicit Differentiation
- 33 Logarithmic Differentiation | Example: x^sinx
- 34 Intro to Related Rates
- 35 Linear Approximations | Using Tangent Lines to Approximate Functions
- 36 The MEAN Value Theorem is Actually Very Nice
- 37 Relative and Absolute Maximums and Minimums | Part I
- 38 Relative and Absolute Maximums and Minimums | Part II
- 39 Using L'Hopital's Rule to show that exponentials dominate polynomials
- 40 Applying L'Hopital's Rule to Exponential Indeterminate Forms
- 41 Ex: Optimizing the Volume of a Box With Fixed Surface Area
- 42 Folding a wire into the largest rectangle | Optimization example
- 43 Optimization Example: Minimizing Surface Area Given a Fixed Volume
- 44 Tips for Success in Flipped Classrooms + OMG BABY!!!
- 45 What's an anti-derivative?
- 46 Solving for the constant in the general anti-derivative
- 47 The Definite Integral Part I: Approximating Areas with rectangles
- 48 The Definite Integral Part II: Using Summation Notation to Define the Definite Integral
- 49 The Definite Integral Part III: Evaluating From The Definition
- 50 "Reverse" Riemann Sums | Finding the Definite Integral Given a Sum
- 51 Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example
- 52 Fundamental Theorem of Calculus II
- 53 Intro to Substitution - Undoing the Chain Rule
- 54 Adjusting the Constant in Integration by Substitution
- 55 Substitution Method for Definite Integrals **careful!**
- 56 Back Substitution - When a u-sub doesn't match cleanly!
- 57 Average Value of a Continuous Function on an Interval
- 58 Exam Walkthrough | Calc 1, Test 3 | Integration, FTC I/II, Optimization, u-subs, Graphing
- 59 ♥♥♥ Thank you Calc Students♥♥♥ Some final thoughts.
