Geometric Examples: Triangles and Functions

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Explores differentiating under the integral sign and continuity of functions in integrals.

Explores Taylor series expansions for derivatives and integrals, with a focus on multiple derivatives and error terms.

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Explores changing variables in double integrals through examples and curvilinear coordinates.

Covers the motivation behind indefinite integrals and the non-injectivity of the derivative operator.

Covers the estimation of integrals using various propositions and demonstrations.

Covers the properties of integrals, including definies integrals, integrables functions, and the theorem of the average.

Covers the definition and properties of integrals of type 2.

Explores the Cauchy-Schwarz inequality in integrals and functions, offering a comprehensive understanding of its applications.

Covers the functions xr, r>0, on [1, +∞], exploring their limits and properties.