# Ex 5.1, 19 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Sept. 17, 2019 by Teachoo

Last updated at Sept. 17, 2019 by Teachoo

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Ex 5.1, 19 (Introduction) Show that the function defined by g (x) = x – [x] is discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x. Greatest Integer less than equal to 𝑥 Ex 5.1, 19 Show that the function defined by g (x) = x – [x] is discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x. Given g(x) = x − 𝑥 Let c be an integer. g (x) is continuous at x = c if L H L = RHL = g (c) i.e.. lim𝑥→𝑐−𝑔 𝑥= lim𝑥→𝑐+𝑔 𝑥=𝑔(𝑐) Hence, L H L ≠ RHL ∴ g (x) is not continuous at x = 6 Hence, g(x) is discontinuous at all integral points. Hence proved

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.