SEAMIC_Functions: Continuity

In this video the concept of continuity in mathematics is discussed. The objectives are to define and understand continuity at a given point, explore different types of discontinuities, and apply these concepts to examples. The definition of continuity involves three conditions: the limit exists, the function exists at the point, and the limit and function values are equal. Different types of discontinuities include finite jumps, infinite jumps, and removable discontinuities, which can be resolved by redefining the function at a specific point. Examples of continuous functions are provided, including polynomials, trigonometric functions, exponential functions, and logarithmic functions. A piecewise-defined function is also analyzed to determine its continuity at a specific point.