Derivatives: Tangents and Secants

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Tangent to Graph of a Function

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

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Covers limits, algebraic operations, and infinite limits with examples of functions' behavior near limit points.

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Introduces derivatives, tangent lines, rules of differentiation, and practical examples.

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Covers elementary functions, derivatives, limits, continuity, and differentiability.

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Revisits the definition of differentiability and the existence of derivatives for functions in open intervals.

Derivatives and Approximations: Logarithmic Functions

Explores derivatives and approximations, focusing on logarithmic functions and their properties.

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Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Analyse I: Summary

Covers real numbers, complex numbers, numerical sequences, series, real functions, function limits, derivatives, Taylor series, integrals, and growth rates of functions.