Taylor Polynomials: Approximating Functions

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Taylor's Formula: Developments and Extrema

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

Analyzing Limits: Indeterminate Forms

Explores handling indeterminate forms in limits through simplification and extracting dominant terms for effective evaluation.

Taylor Polynomial in Two Variables

Covers the Taylor polynomial in two variables and the concept of extrema in functions of several variables.

Gradient and Taylor Formula

Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.

Functions Composition: Continuity & Elements

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.

Functions n+1 Derivatives

Covers the concept of functions being n+1 times differentiable and the Taylor formula.

Analysis I Exam Solutions

Provides solutions to an Analysis I exam, covering various topics.

Linear Approximations: Development Order 2

Covers linear approximations up to order 2 and the Hessian matrix.

Differentiable Functions and Lagrange Multipliers

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

Taylor Series: Basics and Applications

Introduces Taylor series, covering their basics and applications in approximating functions and calculating limits.