https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-2/v/introduction-to-limits-hd 2023-07-27T01:47:53.920337803Z Limits intro In this video, we learn about limits, a fundamental concept in calculus. Limits help us understand what a function approaches as the input gets closer to a certain value, even when the function is undefined at that point. The video demonstrates this concept using two examples with different functions. Sal Khan video https://cdn.kastatic.org/googleusercontent/J1zqnnl2yj2g_ZG6KjF-DQT1hCeNwc1bHWc0qmXwvoFoGSz6w8z729suyX8w6AS3EG4jKcQoDVs6suPJJqryyUSFXw Limits intro In this video, we learn about limits, a fundamental concept in calculus. Limits help us understand what a function approaches as the input gets closer to a certain value, even when the function is undefined at that point. The video demonstrates this concept using two examples with different functions. https://cdn.kastatic.org/ka-youtube-converted/riXcZT2ICjA.mp4/riXcZT2ICjA.mp4 692 Limits from graphs https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-2/a/limits-intro 2022-12-12T02:50:29.790474139Z Limits intro Limits describe how a function behaves near a point, instead of at that point. This simple yet powerful idea is the basis of all of calculus. article https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-2/e/limits-intro 2025-03-01T15:52:37.13987578Z Limits intro Practice finding simple limits and working with limit notation. Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-3/v/limits-from-graphs 2023-07-27T01:47:53.920337803Z Estimating limit values from graphs In this video, we learn to estimate limit values from graphs by observing the function's behavior as x approaches a value from both left and right sides. If the function approaches the same value from both sides, the limit exists. If it approaches different values or is unbounded, the limit doesn't exist. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Estimating limit values from graphs In this video, we learn to estimate limit values from graphs by observing the function's behavior as x approaches a value from both left and right sides. If the function approaches the same value from both sides, the limit exists. If it approaches different values or is unbounded, the limit doesn't exist. https://cdn.kastatic.org/ka-youtube-converted/mols6pMKrto.mp4/mols6pMKrto.mp4 361 Limits from graphs https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-3/e/two-sided-limits-from-graphs 2025-03-01T15:52:37.13987578Z Estimating limit values from graphs Practice finding two sided limits by looking at graphs. Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-3/v/one-sided-limits-from-graphs 2021-04-07T13:36:57Z One-sided limits from graphs A one-sided limit is the value the function approaches as the x-values approach the limit from *one side only*. For example, f(x)=|x|/x returns -1 for negative numbers, 1 for positive numbers, and isn't defined for 0. The one-sided *right* limit of f at x=0 is 1, and the one-sided *left* limit at x=0 is -1. Sal Khan video https://cdn.kastatic.org/googleusercontent/SEllU1FRKAyoX3sR2Nnw6wq86VCrmf7072sms0XlGZv2M66Fp5GcYsSLwk1OQqen3AX4bAOQLvK0IYOHbRocy5w1 One-sided limits from graphs A one-sided limit is the value the function approaches as the x-values approach the limit from *one side only*. For example, f(x)=|x|/x returns -1 for negative numbers, 1 for positive numbers, and isn't defined for 0. The one-sided *right* limit of f at x=0 is 1, and the one-sided *left* limit at x=0 is -1. https://cdn.kastatic.org/ka-youtube-converted/nOnd3SiYZqM.mp4/nOnd3SiYZqM.mp4 551 Limits from graphs https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-3/e/one-sided-limits-from-graphs 2025-03-01T15:52:37.13987578Z One-sided limits from graphs Practice finding one-sided limits by looking at graphs. Tomer Gal exercise