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

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 5.1, 5 Is the function f defined by 𝑓𝑥=𝑥, 𝑖𝑓 𝑥≤1&5, 𝑖𝑓 𝑥>1 continuous at 𝑥 = 0 ? At 𝑥 = 1 ? At 𝑥 = 2 ? Given 𝑓𝑥=𝑥, 𝑖𝑓 𝑥≤1&5, 𝑖𝑓 𝑥>1 At 𝑥 = 0 f is continuous at x = 0 if limx→0 𝑓𝑥= 𝑓0 Hence limx→0 𝑓𝑥=𝑓(0) ⇒ f is continuous at x=0. At 𝒙 = 𝟏 𝑓𝑥=𝑥, 𝑖𝑓 𝑥≤1&5, 𝑖𝑓 𝑥>1 f is continuous at x = 1 if L.H.L = R.H.L = 𝑓1 i.e. limx→1− 𝑓𝑥=limx→1+ 𝑓𝑥=1 Since L.H.L ≠ R.H.L ⇒ f is discontinuous at x=1. At 𝒙 = 𝟐 f is continuous at x = 2 If limx→2 𝑓𝑥= 𝑓2 Hence, limx→𝑐 𝑓𝑥=𝑓2 Hence f is continuous at x=2.

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.