https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-11/v/continuity-at-a-point 2026-06-25T15:40:55.094699315Z Exploring continuity at a point A function f is continuous at a point x=c if we can draw its graph at that point without lifting our pencil. To define this rigorously, f is continuous at x=c if the two-sided limit of f(x) as x approaches c exists and matches the value of f(c). video https://cdn.kastatic.org/ka_thumbnails_cache/d081a155-a915-4f1a-9aa5-ecbbd8577290_1280_720_base.png Exploring continuity at a point A function f is continuous at a point x=c if we can draw its graph at that point without lifting our pencil. To define this rigorously, f is continuous at x=c if the two-sided limit of f(x) as x approaches c exists and matches the value of f(c). https://cdn.kastatic.org/ka-youtube-converted/3KMqU5j7irw.mp4/3KMqU5j7irw.mp4 496 Defining continuity at a point https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-11/v/continuity-at-a-point-graphically 2026-06-25T15:40:55.094699315Z Working an example: Continuity at a point (graphical) In this video, we explore the necessary conditions for continuity at a point using graphical representations of functions. We analyze two examples to determine if the left-hand and right-hand limits exist, if the function is defined at the point, and then we use these observations to determine if the function is continuous at that point. video https://cdn.kastatic.org/googleusercontent/wWWKX4O1MRQ791Lu002NWdcZcwM4odbnGNjmL2I3xEJWgXIkfvxK1ErY1iZcHeQyBYr9ftz1MMtxCdfycQMk80E Working an example: Continuity at a point (graphical) In this video, we explore the necessary conditions for continuity at a point using graphical representations of functions. We analyze two examples to determine if the left-hand and right-hand limits exist, if the function is defined at the point, and then we use these observations to determine if the function is continuous at that point. https://cdn.kastatic.org/ka-youtube-converted/jzn4rTPajT0.mp4/jzn4rTPajT0.mp4 439 Defining continuity at a point https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-11/e/analyze-continuity-at-a-point-graphically 2025-04-23T04:17:28.661677998Z Continuity at a point (graphical) Given the graph of a function and a specific point, analyze whether the function is continuous at that point. Tomer Gal exercise