https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:basic-calculus/x09646558c1ff0797:limits/v/limit-by-substitution 2025-01-06T10:18:43.365910625Z प्रत्यक्ष प्रतिस्थापन द्वारा सीमा ज्ञात करना (Limits by direct substitution) Sal explains how you can easily find limits of functions at points where the functions are continuous: simply plug in the x-value into the function! Later we will learn how to find limits even when the function isn't continuous. video https://cdn.kastatic.org/ka_thumbnails_cache/de57d77c-2ca0-46dc-8d5a-a313b891f121_1280_720_base.png प्रत्यक्ष प्रतिस्थापन द्वारा सीमा ज्ञात करना (Limits by direct substitution) Sal explains how you can easily find limits of functions at points where the functions are continuous: simply plug in the x-value into the function! Later we will learn how to find limits even when the function isn't continuous. https://cdn.kastatic.org/ka-youtube-converted/wDMlUVK-17Q.mp4/wDMlUVK-17Q.mp4 127 बहुपदों और परिमय फलनों की सीमाएँ (Limits of polynomials and rational functions) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:limits-of-polynomials-and-rational-functions/v/undefined-limit-by-substitution 2025-01-06T10:18:43.365910625Z प्रत्यक्ष प्रतिस्थापन द्वारा अपरिभाषित सीमाएं (Undefined limits by direct substitution) Sal gives an example of a limit where direct substitution ends in a quotient with 0 in the denominator and non-0 in the numerator. Such limits are undefined. What about limits where substitution ends in 0/0? Keep going and you'll see! video https://cdn.kastatic.org/ka_thumbnails_cache/4a9590f4-bf01-48e5-a2a6-0f2e0397a886_1280_720_base.png प्रत्यक्ष प्रतिस्थापन द्वारा अपरिभाषित सीमाएं (Undefined limits by direct substitution) Sal gives an example of a limit where direct substitution ends in a quotient with 0 in the denominator and non-0 in the numerator. Such limits are undefined. What about limits where substitution ends in 0/0? Keep going and you'll see! https://cdn.kastatic.org/ka-youtube-converted/RMKkPA_37Ik.mp4/RMKkPA_37Ik.mp4 134 बहुपदों और परिमय फलनों की सीमाएँ (Limits of polynomials and rational functions) https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:basic-calculus/x09646558c1ff0797:limits/e/find-limits-by-direct-substitution 2025-04-09T10:40:17.096567662Z प्रत्यक्ष प्रतिस्थापन द्वारा सीमा ज्ञात करना (Limits by direct substitution) बिंदु को सीधे फलन में प्रविष्ट करके विशिष्ट बिंदुओं पर फलन की सीमाएं ज्ञात करें। Tomer Gal exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:limits-of-polynomials-and-rational-functions/e/identify-undefined-limits-by-direct-substitution 2025-04-11T17:56:27.951539611Z ऐसी सीमाओं के साथ प्रत्यक्ष प्रतिस्थापन जिनका अस्तित्व नहीं हैं प्रत्यक्ष प्रतिस्थापन द्वारा सीमाएँ निर्धारित करें। सीमाएँ अस्तित्वहीन हो सकती हैं। Tomer Gal exercise https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:basic-calculus/x09646558c1ff0797:limits/v/limit-example-1 2025-01-06T10:18:43.365910625Z गुणनखंड द्वारा सीमाएं (Limits by factoring) In this video, we explore the limit of (x²+x-6)/(x-2) as x approaches 2. By factoring and simplifying the expression, we discover that the function is undefined at x = 2, but its limit from both sides as x approaches 2 is in fact 5. Sal Khan video https://cdn.kastatic.org/googleusercontent/D5DvW40fHhxKEOVQeAGWJsz4bfCOxL4VtwJY2M7b3X8pjYFCZfhoK5ges5woh73cAcug89AM9CA9xXZNY-8DfQKG गुणनखंड द्वारा सीमाएं (Limits by factoring) In this video, we explore the limit of (x²+x-6)/(x-2) as x approaches 2. By factoring and simplifying the expression, we discover that the function is undefined at x = 2, but its limit from both sides as x approaches 2 is in fact 5. https://cdn.kastatic.org/ka-youtube-converted/1u7n9XFU614.mp4/1u7n9XFU614.mp4 344 बहुपदों और परिमय फलनों की सीमाएँ (Limits of polynomials and rational functions) https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:basic-calculus/x09646558c1ff0797:limits/e/two-sided-limits-using-algebra 2025-04-09T10:40:17.096567662Z गुणनखंड द्वारा सीमाएं (Limits by factoring) बीजगणितीय रूप से फलनों को सरल करके दो-तरफा सीमाएँ ज्ञात करने का अभ्यास करें। Tomer Gal exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:limits-of-polynomials-and-rational-functions/v/limit-of-piecewise-defined-functions 2025-06-25T04:36:24.163902917Z खण्डों में परिभाषित फलनों की सीमा In this video, we'll find limits for some piecewise defined functions. For the first problem, we find the limit at two points - one where the function retains it definition and another where the definition changes. For the next two problems, we find the missing values given that the limit exists. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw खण्डों में परिभाषित फलनों की सीमा In this video, we'll find limits for some piecewise defined functions. For the first problem, we find the limit at two points - one where the function retains it definition and another where the definition changes. For the next two problems, we find the missing values given that the limit exists. https://cdn.kastatic.org/ka-youtube-converted/urP8fbekQWk.mp4/urP8fbekQWk.mp4 487 बहुपदों और परिमय फलनों की सीमाएँ (Limits of polynomials and rational functions) https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:basic-calculus/x09646558c1ff0797:limits/v/limits-of-piecewise-functions 2025-01-06T10:18:43.365910625Z खण्डश: फलनों की सीमाएं (Limits of piecewise functions) In this video, we explore limits of piecewise functions using algebraic properties of limits and direct substitution. We learn that to find one-sided and two-sided limits, we need to consider the function definition for the specific interval we're approaching and substitute the value of x accordingly. video https://cdn.kastatic.org/googleusercontent/MN8eQ6wHnZSXGRVLTSSXGf05-TPQ15QbYTU2fvwXRXySaSNxTYGX--GyeGctHs6wJRM1_WF5xoxq2zh8EJrD_Q0 खण्डश: फलनों की सीमाएं (Limits of piecewise functions) In this video, we explore limits of piecewise functions using algebraic properties of limits and direct substitution. We learn that to find one-sided and two-sided limits, we need to consider the function definition for the specific interval we're approaching and substitute the value of x accordingly. https://cdn.kastatic.org/ka-youtube-converted/xv8sUHTGT3s.mp4/xv8sUHTGT3s.mp4 229 बहुपदों और परिमय फलनों की सीमाएँ (Limits of polynomials and rational functions) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:limits-of-polynomials-and-rational-functions/v/limits-challenge-problem 2025-06-25T04:36:24.163902917Z सीमाएं (चुनौतीपूर्ण प्रश्न) In this video, we'll tackle a challenging problem from the world of limits. We're given the value of limit of a function at a particular point and we need to find the limit of a different function at the same point. We'll first look at an intuitive hunch for what the missing value could be. We'll then find limit from both sides and make sense of what the missing value could be. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw सीमाएं (चुनौतीपूर्ण प्रश्न) In this video, we'll tackle a challenging problem from the world of limits. We're given the value of limit of a function at a particular point and we need to find the limit of a different function at the same point. We'll first look at an intuitive hunch for what the missing value could be. We'll then find limit from both sides and make sense of what the missing value could be. https://cdn.kastatic.org/ka-youtube-converted/oAD5UkUdrIE.mp4/oAD5UkUdrIE.mp4 326 बहुपदों और परिमय फलनों की सीमाएँ (Limits of polynomials and rational functions) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:limits-of-polynomials-and-rational-functions/v/limit-of-x-n-a-n-x-a 2025-06-25T04:36:24.163902917Z (x^n - a^n) / (x - a) की सीमा In this video, we learn about a formula for limits that help us work with difference of powers. We first understand the formula, then derive it using binomial theorem before solving problems involving direct application and minor manipulation. We then generalise the formula for all rational values of n. We finally tackle a problem that uses the generalised version of the formula. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw (x^n - a^n) / (x - a) की सीमा In this video, we learn about a formula for limits that help us work with difference of powers. We first understand the formula, then derive it using binomial theorem before solving problems involving direct application and minor manipulation. We then generalise the formula for all rational values of n. We finally tackle a problem that uses the generalised version of the formula. https://cdn.kastatic.org/ka-youtube-converted/Gk_amsB9h-c.mp4/Gk_amsB9h-c.mp4 407 बहुपदों और परिमय फलनों की सीमाएँ (Limits of polynomials and rational functions) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:limits-of-polynomials-and-rational-functions/v/limit-at-a-point-of-discontinuity 2025-01-06T10:18:43.365910625Z खण्डश: फलनों की सीमाएं : निरपेक्ष मान (Limits of piecewise functions: absolute value) This video focuses on finding the limit of |x-3|/(x-3) at x=3 by rewriting it and examining it as a piecewise function. This approach helps us understand the behavior of the function for x values greater or less than 3, revealing that the limit doesn't exist. Sal Khan video https://cdn.kastatic.org/googleusercontent/N0HK96ZJm1B6MqIbh_Od4csow9B9ZvbMimpUgBSgjRseNCTD4gpwvpNYTnWWc5_w7o1FzFH0mIha_5Uf0ZvrOhsfZQ खण्डश: फलनों की सीमाएं : निरपेक्ष मान (Limits of piecewise functions: absolute value) This video focuses on finding the limit of |x-3|/(x-3) at x=3 by rewriting it and examining it as a piecewise function. This approach helps us understand the behavior of the function for x values greater or less than 3, revealing that the limit doesn't exist. https://cdn.kastatic.org/ka-youtube-converted/64xJTmuU6v0.mp4/64xJTmuU6v0.mp4 380 बहुपदों और परिमय फलनों की सीमाएँ (Limits of polynomials and rational functions)