Question 17 - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 13, 2024 by Teachoo

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Question 17 The function 𝑓:𝑅→𝑍 defined by 𝑓(𝑥)=[𝑥]; where [⋅] denotes the greatest integer function, is (A) Continuous at 𝒙=𝟐.𝟓 but not differentiable at 𝒙=𝟐.𝟓 (B) Not Continuous at 𝒙=𝟐.𝟓 but differentiable at 𝒙=𝟐.𝟓 (C) Not Continuous at 𝒙=𝟐.𝟓 and not differentiable at 𝒙=𝟐.𝟓 (D) Continuous as well as differentiable at 𝒙=𝟐.𝟓Let’s draw the graph We note that At integer points, [x] is not continuous At non integer points, [x] is continuous and differentiable Therefore, [x] is continuous and differentiable both at x = 2.5 So, the correct answer is (D)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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