Continuous Functions and Elementary Functions

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Covers the resolution of triangles using trigonometric functions and the importance of cosine and sine theorems.

Focuses on determining the derivability of functions within their domains using square roots, logarithmic, and exponential functions.

Explores trigonometric addition theorem, double angles, and tangent properties.

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Explores the symmetries of trigonometric functions, periodicity, and properties of even and odd functions.

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

Explores approximating functions with polynomials using Taylor series and discusses the convergence of series representations.

Explores the rotation of vectors in a plane using trigonometric functions.

Explores limits, continuity, and uniform continuity in functions, including properties at specific points and closed intervals.

Explores fundamental special functions with applications in various fields.