Example 9 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 9 Discuss the continuity of the function f defined by 𝑓 (𝑥) = 1/𝑥 , 𝑥 ≠ 0. Given 𝑓 (𝑥) = 1/𝑥 At 𝒙 = 𝟎 𝑓 (0) = 1/0 = ∞ Hence, 𝑓(𝑥) is not defined at 𝒙=𝟎 By definition, 𝑓 (𝑥) = 1/𝑥 , 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 , (𝐥𝐢𝐦)┬(𝐱→𝒄) 𝒇(𝒙)=𝒇(𝒄) L.H.S L.H.S (𝐥𝐢𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = lim┬(x→𝑐) 1/𝑥 Putting 𝑥 =𝑐 = 1/𝑐 R.H.S 𝒇(𝒄) =1/𝑐 " " Since, L.H.S = R.H.S ∴ Function is continuous at x = c (Except 0) Since, L.H.S = R.H.S ∴ Function is continuous at x = c (Except 0) Thus, we can write that f is continuous for all 𝒙 ∈𝐑−{𝟎}
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About the Author
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