Taylor Polynomials: Definition and Approximation

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Development Limit: Order 1 and 2

Covers limited order 1 and 2 development, focusing on linearity and polynomial approximation.

Taylor Development: Higher Derivatives

Covers the calculation of Taylor polynomials, higher derivatives, and Taylor series using examples.

Approximation of Functions by Taylor Polynomials

Explores the theory and application of Taylor polynomials for function approximation and limit calculations.

Advanced Analysis I - Taylor's Formula Corollary

Explores the corollary of Taylor's formula for function approximation around a point.

Taylor Polynomials: Approximating Functions

Introduces Taylor polynomials for approximating functions around a point, showcasing their importance in accurately representing functions.

Taylor Polynomials and Approximations

Explores Taylor polynomials and approximations for various functions, emphasizing derivative equality and polynomial development around a specific point.

Taylor Polynomials: Calculating Limits and Derivatives

Covers the calculation of Taylor polynomials and their applications in limits and derivatives of functions from R² to R.

Taylor Polynomials: Approximating Functions with Taylor Polynomials

Delves into Taylor polynomials, showcasing how higher orders improve function approximations and how they can be used to calculate limits.

Taylor Polynomials: Examples and Convergence

Covers examples of Taylor polynomials and discusses their convergence when approximating functions.

Taylor Polynomials Exercise

Covers the calculation of Taylor polynomials and error bounds for function approximation.