https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:continuity-and-differentiability-ncert-new/x6f66cbee9a2f805b:continuity/v/limits-to-define-continuity 2020-07-26T09:23:41Z Continuity introduction Sal introduces a formal definition of continuity at a point using limits. Sal Khan video https://cdn.kastatic.org/googleusercontent/lqWE1TP7dxuKS8OMgoNbtpUvHP_wOQici-nojNQvxxwIAN7CDEps48SI4lX6RVCgsI_Mt7_m9RODOEG5Chw5nZXAig Continuity introduction Sal introduces a formal definition of continuity at a point using limits. https://cdn.kastatic.org/ka-youtube-converted/kdEQGfeC0SE.mp4/kdEQGfeC0SE.mp4 674 Continuity https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-11/v/continuity-at-a-point 2024-07-16T13:29:53.845179388Z 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 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 Continuity https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-11/v/continuity-at-a-point-graphically 2023-07-27T02:34:53.22139958Z Worked 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 Worked 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 Continuity 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 https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-12/v/continuity-over-an-interval 2022-10-07T00:22:18.752150461Z Continuity over an interval A function ƒ is continuous over the open interval (a,b) if and only if it's continuous on every point in (a,b). ƒ is continuous over the closed interval [a,b] if and only if it's continuous on (a,b), the right-sided limit of ƒ at x=a is ƒ(a) and the left-sided limit of ƒ at x=b is ƒ(b). video https://cdn.kastatic.org/ka_thumbnails_cache/38dbc9a0-1ea9-4cd8-b7b5-d17ef4b4f940_1280_720_base.png Continuity over an interval A function ƒ is continuous over the open interval (a,b) if and only if it's continuous on every point in (a,b). ƒ is continuous over the closed interval [a,b] if and only if it's continuous on (a,b), the right-sided limit of ƒ at x=a is ƒ(a) and the left-sided limit of ƒ at x=b is ƒ(b). https://cdn.kastatic.org/ka-youtube-converted/ENIQiqxFpBc.mp4/ENIQiqxFpBc.mp4 540 Continuity https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-12/e/continuous-functions--graphs 2025-04-23T04:17:28.661677998Z Continuity over an interval Given the graphs of two functions, determine which function is continuous over a given interval. Tomer Gal exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:continuity-and-differentiability-ncert-new/x6f66cbee9a2f805b:continuity/e/continuity-challenge 2026-04-07T22:59:30.107127435Z Continuity challenge Review your understanding of continuity with some challenge problems. Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-13/e/continuity 2025-04-23T04:17:28.661677998Z Removable discontinuities Remove discontinuity points of piecewise functions by assigning appropriate values. Tomer Gal exercise