# Example 9 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 9 Discuss the continuity of the function f defined by 𝑓 (𝑥) = 1𝑥 , 𝑥 ≠ 0. Given 𝑓 (𝑥) = 1𝑥 At 𝑥 = 0 𝑓 (𝑥) = 1𝑥 𝑓 (0) = 10 = Hence 𝑓 (𝑥) is not defined at 𝑥 = 0 By definition, 𝑓 (𝑥) = 1𝑥 , 𝑥 ≠ 0. So, we check for continuity at all points except 0. Let c be any real number except 0. f is continuous at 𝑥 =𝑐 if , limx→𝑐 𝑓𝑥=𝑓𝑐 Thus limx→𝑐 𝑓𝑥=𝑓𝑐 ⇒ f is continuous at 𝑥 =𝑐 (Except 0) f is not continuous for all 𝒙 ∈𝐑−{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.