Why Taylor Series actually work: The Taylor Inequality

გაკვეთილები52 გაკვეთილი

• ✓1Welcome to Calculus II
• ✓2Intro to Integration By Parts --- Examples: ∫xsinxdx & ∫arctan(x)dx
• ✓3Two Tricky Integration By Parts Examples
• ✓4Trigonometric Integrals --- ∫sin^n(x)cos^m(x)dx via Pythagorean or Half-Angle Identities
• ✓5Intro to Trigonometric Substitution --- Ex: Deriving Area of Circle Formula
• ✓6Trig Subs | How To Choose The Substitution & Deal With Indefinite Integrals
• ✓7Deconstructing a messy integral | Trig subs & u-subs combined
• ✓8Integration by Partial Fractions | Big Idea + First Example
• ✓9Partial Fractions | Repeating and irreducible Quadratic Terms
• ✓10Choosing what integration methods to use - Part I
• ✓11Choosing what integration methods to use - Challenging Example!
• ✓12MATH PROF vs TRICKY INTEGRALS
• ✓13Improper Integrals: How to Integrate with Infinities, 2 ways!
• ✓14Comparison Test for Improper Integrals
• ✓15Arclength Formula | Derivation & Ex: Circumference of a Circle
• ✓16Area of Surfaces of Revolution | Derivation & Example
• ✓17Infinite Surface Area but Finite Volume!?!? *Gabriel's Horn*
• ✓18Intro to Sequences
• ✓19Limits of Sequences, Limit laws & Function Representations
• ✓20The Hierarchy of Big Functions || n^n greater than n! greater than e^n greater than n^100
• ✓21Intro to Series: What is 1/2+1/4+1/8+1/16+...?
• ✓22Geometric Series | Convergence, Derivation, and Example
• ✓23Harmonic Series | It diverges, but insanely slowly!
• ✓24Integral Test | Derivation & 1st Example
• ✓25Estimating the Remainder of a Series Approximation via the Integral Test
• ✓26Comparison Test for Series
• ✓27Limit Comparison Test for Series
• ✓28Alternating Series Test | Intuition, Statement & Example
• ✓29Alternating Series | Estimating the Remainder
• ✓30The bizarre world of INFINITE rearrangements // Riemann Series Theorem
• ✓31Absolute Convergence vs Conditional Convergence vs Convergence
• ✓32Ratio & Root Tests | Geometric Series Generalized
• ✓33Choosing Which Convergence Test to Apply to 8 Series
• ✓34Solving Inequalities with Absolute Values: Ex |x-2| less than 3
• ✓35Power Series & Intervals of Convergence
• ✓36Intro to Taylor Series: Approximations on Steroids
• ✓373 Applications of Taylor Series: Integrals, Limits, & Series
• ✓38Why Taylor Series actually work: The Taylor Inequality
• ✓39Plotting Parametric Curves
• ✓40Tangents to Parametric Curves | Multiple tangents at the same point!!
• ✓41Area under a Parametric Curve | Formula, Derivation, & Example
• ✓42Arclength of Parametric Curves
• ✓43Intro to Polar Coordinates
• ✓44Sketching Polar Curves
• ✓45Areas in Polar Coordinates
• ✓46Example: Area Inside Polar Curves
• ✓47Why Exponential Growth?? Intro to Separable Differential Equations
• ✓48Defining the Natural Logarithm as an Integral?!?!?
• ✓49Intro to COMPLEX NUMBERS // Motivation, Algebraic Definition & Fundamental Theorem of Algebra Ep. 1
• ✓50The geometric view of COMPLEX NUMBERS
• ✓51The Polar Form of COMPLEX NUMBERS // Finding the nth roots of -1
• ✓52Why hyperbolic functions are actually really nice

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