https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:continuity-of-different-functions/v/continuity-of-polynomial-functions 2025-06-25T04:37:22.958747522Z बहुपद फलनों का सांतत्य In this video, we'll take things from concrete to abstract. We'll start by testing continuity at two points for a simple polynomial functions. We'll then test the continuity of that function across its domain. We'll finally zoom out and test the continuity of all polynomial functions for all points in their domain. Before this final step, we'll take a refresher on what polynomial functions are along with looking at a number of examples. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw बहुपद फलनों का सांतत्य In this video, we'll take things from concrete to abstract. We'll start by testing continuity at two points for a simple polynomial functions. We'll then test the continuity of that function across its domain. We'll finally zoom out and test the continuity of all polynomial functions for all points in their domain. Before this final step, we'll take a refresher on what polynomial functions are along with looking at a number of examples. https://cdn.kastatic.org/ka-youtube-converted/t3DUqtUjwVQ.mp4/t3DUqtUjwVQ.mp4 452 विभिन्न फलनों का सांतत्य https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:continuity-of-different-functions/v/continuity-of-rational-functions 2025-06-25T04:37:22.958747522Z परिमेय फलनों का सांतत्य In this video, we'll discuss continuity of two rational functions. Before we solve problems, we'll refresh the definition of rational functions. For the first function, we find the limits at x = 0 and x = 5 for 1 by (x-5). For the second function, we find the limits at x = -5 for (x^2 - 25) by (x + 5). In both of these problems, we're looking at points where the function is not defined. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw परिमेय फलनों का सांतत्य In this video, we'll discuss continuity of two rational functions. Before we solve problems, we'll refresh the definition of rational functions. For the first function, we find the limits at x = 0 and x = 5 for 1 by (x-5). For the second function, we find the limits at x = -5 for (x^2 - 25) by (x + 5). In both of these problems, we're looking at points where the function is not defined. https://cdn.kastatic.org/ka-youtube-converted/K8YCWGICVOI.mp4/K8YCWGICVOI.mp4 475 विभिन्न फलनों का सांतत्य https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:continuity-of-different-functions/v/continuity-of-greatest-integer-function 2025-06-25T04:37:22.958747522Z महत्तम पूर्णांक फलन का सांतत्य In this video, we'll talk about continuity of greatest integer function. We'll first plot its graph and try to figure out points of discontinuity visually. We'll then make separate cases - for integers and non-integers - and evaluate continuity for both. Finally, we'll solve a problem where we use the definition of GIF to prove discontinuity at integral points of a different function. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw महत्तम पूर्णांक फलन का सांतत्य In this video, we'll talk about continuity of greatest integer function. We'll first plot its graph and try to figure out points of discontinuity visually. We'll then make separate cases - for integers and non-integers - and evaluate continuity for both. Finally, we'll solve a problem where we use the definition of GIF to prove discontinuity at integral points of a different function. https://cdn.kastatic.org/ka-youtube-converted/HmTx1pUbe1w.mp4/HmTx1pUbe1w.mp4 521 विभिन्न फलनों का सांतत्य https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:continuity-of-different-functions/v/algebra-of-continuous-functions 2025-06-25T04:37:22.958747522Z संतत फलनों का बीजगणित In this video, we'll cover algebra of continuous functions. Just like we could do things in the world of limits, we can add, subtract, multiply, and divide continuous functions. The resultant functions are also continuous wherever they are defined. We prove this for the case of addition before solving a worked example. We also take a look at how the algebra of continous functions works in the world of trigonometry. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw संतत फलनों का बीजगणित In this video, we'll cover algebra of continuous functions. Just like we could do things in the world of limits, we can add, subtract, multiply, and divide continuous functions. The resultant functions are also continuous wherever they are defined. We prove this for the case of addition before solving a worked example. We also take a look at how the algebra of continous functions works in the world of trigonometry. https://cdn.kastatic.org/ka-youtube-converted/GifI2QzKB4M.mp4/GifI2QzKB4M.mp4 427 विभिन्न फलनों का सांतत्य https://hi.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-2/x6a634f0b79812b7f:continuity-and-differentiability/v/continuity-of-trigonometric-functions 2025-06-25T04:37:22.958747522Z त्रिकोणमितीय फलनों का सांतत्य We prove using limits the continuity of trigonometric functions. We use trigonometric identities to prove continuity for sin(x) and cos(x). We use algebra of limits to prove continuity for tan(x) and cot(x). We also figure out the points of discontinuity of functions other than sin(x) and cos(x). Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw त्रिकोणमितीय फलनों का सांतत्य We prove using limits the continuity of trigonometric functions. We use trigonometric identities to prove continuity for sin(x) and cos(x). We use algebra of limits to prove continuity for tan(x) and cot(x). We also figure out the points of discontinuity of functions other than sin(x) and cos(x). https://cdn.kastatic.org/ka-youtube-converted/BujMe-JECVc.mp4/BujMe-JECVc.mp4 527 विभिन्न फलनों का सांतत्य https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:continuity-of-different-functions/v/continuity-of-composite-functions 2025-06-25T04:37:22.958747522Z संयुक्त फलनों का सांतत्य In this video, we understand how to check continuity of composite functions. We do this using the example of sin(x^2). We first visually observe the continuity. We then find the continuity at a point, then generalise it for all composite functions. Finally, we use this technique to check continuity of functions involving modulus and trigonometric functions. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw संयुक्त फलनों का सांतत्य In this video, we understand how to check continuity of composite functions. We do this using the example of sin(x^2). We first visually observe the continuity. We then find the continuity at a point, then generalise it for all composite functions. Finally, we use this technique to check continuity of functions involving modulus and trigonometric functions. https://cdn.kastatic.org/ka-youtube-converted/WXESNxUHR3M.mp4/WXESNxUHR3M.mp4 408 विभिन्न फलनों का सांतत्य