Intro to Taylor Series: Approximations on Steroids

While in Calc I we used Linear Approximations, can we approximate functions by quadratics, cubics, etc? Indeed, Taylor Series (and Maclauren series when they are centered at x=0) provide a method for effective approximation of functions locally. And the best part is all we need to know is a lot of information about derivatives all at one point, and this is enough to get, typically, a decent approximation locally.

►Full Course Playlist: CALCULUS II:    • Calculus II (Integration Methods, Series, ...  

♡♡♡SUPPORT THE CHANNEL♡♡♡
►Support on PATREON:   / drtrefor  
►MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett
►CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes

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:
►Cool Math Series:
   • Cool Math Series  
►Learning Math Series:
   • 5 Tips To Make Math Practice Problems Actu...  
►LaTeX:    • Intro to LaTeX **Full Tutorial**  Part II ...  

SOCIALS:
►X/Twitter: http://X.com/treforbazett
►TikTok:   / drtrefor  
►Instagram (photography based):   / treforphotography