Derivability and Continuity

This lecture covers the concepts of continuity and derivability of functions, emphasizing the conditions for a function to be continuous and differentiable at a point. It also explores the relationship between continuity and differentiability through theorems and examples, illustrating the importance of these concepts in mathematical analysis. The lecture further delves into linear approximation, discussing how tangent lines can be used to approximate function values near a point on the graph. Various examples are provided to demonstrate the application of linear approximation in calculating function values. The lecture concludes with a detailed explanation of linear approximation and its significance in mathematical analysis.