Taylor Series: Development and Applications

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Related lectures (31)

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Application of Taylor's approximation formula

Covers the application of Taylor's formula, including composition of functions and detecting local extrema.

Taylor's Formula: Developments and Applications

Explores Taylor's formula, polynomials, functions, and series applications.

Taylor Series and Function Analysis

Explores Taylor series, function properties, inflection points, and critical points in graphical and mathematical contexts.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Derivatives and Convexity

Explores derivatives, local extrema, and convexity in functions, including Taylor's formula and function compositions.

Taylor Polynomials: Special Cases

Explores Taylor polynomials, odd orders, simplification, residues, and special cases of zero polynomials.

Taylor's Formula: Developments and Extrema

Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.

Taylor's Formula: Convexity, Inflection Points

Explores Taylor's formula, uniqueness of Taylor series, Mean Value Theorem, inflection points, and convexity.

Nature of Extremum Points

Explores the nature of extremum points in functions of class e² around the point (0,0), emphasizing the importance of understanding their behavior in the vicinity.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.