CONCEPT MAP.

The article focuses on the concepts of continuity and differentiability in mathematical functions. A function is defined as continuous at a point if the limits from both sides equal the function's value at that point. Differentiability at a point requires the existence of both left-hand and right-hand derivatives that are equal. The text also outlines types of discontinuities, including jump, oscillating, and removable discontinuities, and provides standard derivatives and rules for differentiating various types of functions, such as composite, implicit, and parametric functions. Additionally, it discusses the Binomial Theorem and its applications for both fractional and integral indices, including properties and coefficients related to binomial expansions. [Extracted from the article]