Slide43.JPG

Slide44.JPG

 

Go Ad-free

Transcript

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)

Davneet Singh's photo - Co-founder, Teachoo

Made by

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, Social Science, Physics, Chemistry, Computer Science at Teachoo.