Taylor Polynomials: Definition and Approximation

This lecture introduces Taylor polynomials as a method to approximate functions like sin, cos, exp, ln, sinh, and √. By using the tangent line at a point, Taylor polynomials provide calculable values such as π, sin(1), e = exp(1), and √5. The process involves adjusting coefficients to match function values and derivatives at a specific point, resulting in improved approximations. Higher polynomial degrees lead to better graph fitting around the point of approximation. The lecture also covers the general properties and examples of Taylor polynomials, showcasing their versatility in approximating various functions.