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Lecture# Derivatives and Continuity

Description

This lecture covers the concept of derivatives and continuity, focusing on the derivative of a function and its continuity on an interval. It explains the identity by the derivative, the reciprocal function, and provides examples of functions like exponential and trigonometric functions.

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Related concepts (118)

In course

List of trigonometric identities

In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle. These identities are useful whenever expressions involving trigonometric functions need to be simplified.

Trigonometry

Trigonometry () is a branch of mathematics concerned with relationships between angles and ratios of lengths. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation.

Theta function

In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field theory. The most common form of theta function is that occurring in the theory of elliptic functions. With respect to one of the complex variables (conventionally called z), a theta function has a property expressing its behavior with respect to the addition of a period of the associated elliptic functions, making it a quasiperiodic function.

CD-i

The Compact Disc-Interactive (CD-I, later CD-i) is a digital optical disc data storage format that was mostly developed and marketed by Dutch company Philips. It was created as an extension of CDDA and CD-ROM and specified in the Green Book specifications, co-developed by Philips and Sony, to combine audio, text and graphics. The two companies initially expected to impact the education/training, point of sale, and home entertainment industries, but CD-i eventually became best known for its video games.

CD-ROM

A CD-ROM (ˌsiːdiːˈrɒm, compact disc read-only memory) is a type of read-only memory consisting of a pre-pressed optical compact disc that contains data. Computers can read—but not write or erase—CD-ROMs. Some CDs, called enhanced CDs, hold both computer data and audio with the latter capable of being played on a CD player, while data (such as software or digital video) is only usable on a computer (such as ISO 9660 format PC CD-ROMs).

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles d'une variable.

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