# Example 3

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 3 Discuss the continuity of the function f given by 𝑓(𝑥) = | 𝑥 | 𝑎𝑡 𝑥 = 0. 𝑓(𝑥) = |𝑥| 𝑓𝑥= −𝑥, 𝑖𝑓 𝑥<0𝑥, 𝑖𝑓 𝑥 ≥0 f is continuous at 𝑥 = 0 if L.H.L = R.H.L = 𝑓(0) i.e. limx→0− 𝑓𝑥=limx→0+ 𝑓𝑥=𝑓(0) So, L.H.L = R.H.L & 𝑓(0) = |0| = 0. Hence, limx→0− 𝑓𝑥=limx→0+ 𝑓𝑥=𝑓(0) ∴ f is continuous at 𝒙 = 𝟎

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About the Author

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.