Explore the fundamental concepts of continuity and differentiability in calculus through this comprehensive 33-minute video tutorial. Learn to identify points of discontinuity, including holes, jump discontinuities, and infinite discontinuities, and master the 3-step continuity test. Discover the relationship between continuity and differentiability, and analyze functions using one-sided limits. Gain practical experience with numerous examples and practice problems, focusing on piecewise functions and their graphical representations. Understand the characteristics of differentiable functions, including smooth curves and points of non-differentiability such as sharp turns, cusps, and vertical tangents. Enhance your calculus skills with clear explanations and visual aids to solidify your understanding of these crucial mathematical concepts.