The most important limit in Calculus // Geometric Proof & Applications скачать в хорошем качестве

The most important limit in Calculus // Geometric Proof & Applications

►Get my favorite, free calculator app for your phone or tablet: MAPLE CALCULATOR: https://www.maplesoft.com/products/ma... ►Check out MAPLE LEARN for your browser to make beautiful graphs and much more: https://www.maplesoft.com/products/le... ►Check out Maplesoft's YouTube channel:    / @maplesoft   The limit of sin(x)/x as x goes to zero is perhaps the most important limit in Calculus and it is just one! This is equivalent to the small angle approximation that sin(x) is approximately just equal to x when x is sufficiently small. In this video we will begin with an application from astronomy using angular distance to estimate the size of objects in the universe. Then we will focus on the geometric proof of the limit of sin(x)/x which follows from some simple trigonometry. It is important to proof this geometrically because we can't just use L'Hopitals rule as that requires knowing that the derivative of sin(x) is just cos(x). As we will see, that proof however relies on this very limit! Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pag... 0:00 Limit of sin(x)/x as x goes to 0 0:56 Astronomy Application 2:49 Visual Intuition using Maple Learn 3:47 Geometric Proof 8:16 Proof that the derivative of sin(x) is cos(x) COURSE PLAYLISTS: ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...   ► CALCULUS II:    • Calculus II (Integration Methods, Series, ...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus (Vect...   ►VECTOR CALCULUS (Calc IV)    • Calculus IV: Vector Calculus (Line Integra...   ►DIFFERENTIAL EQUATIONS:    • Ordinary Differential Equations (ODEs)   ►LAPLACE TRANSFORM:    • Laplace Transforms and Solving ODEs   ►GAME THEORY:    • Game Theory   OTHER PLAYLISTS: ► Learning Math Series    • 5 Tips To Make Math Practice Problems Actu...   ►Cool Math Series:    • Cool Math Series   BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based):   / treforbazett   ►Instagram (photography based):   / treforphotography