Gudermannian function

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Covers hyperbolic functions, including definitions, properties, and derivatives, explained with detailed examples and derivations.

Hyperbolic Functions

Explores hyperbolic functions, their properties, and derivatives, including tanh(x) and arctanh(x).

Differential Calculation: Hyperbolic Functions

Explores differential calculation with hyperbolic functions and Taylor series, emphasizing the importance of signed areas in integrals.

Complex Hyperbolic and Trigonometric Functions

Explores complex hyperbolic and trigonometric functions, defining key properties and relationships with exponential functions.

Composition of Taylor Expansions

Covers the computation of Taylor expansions composition up to order 4.

Inverse Hyperbolic Functions: Examples

Covers examples of inverse hyperbolic functions and their applications in solving mathematical problems.

Hyperbolic Functions: Tangent and Cotangent

Covers the definitions and examples of hyperbolic tangent and cotangent functions.

Limits and Continuity

Explores limits, continuity, and function characterization, emphasizing the preservation of continuity and the importance of understanding restrictions.

Reciprocal Trigonometric Functions

Explores reciprocal trigonometric functions, hyperbolic functions, and area theorems.

Derivatives and Reciprocal Functions

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.