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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.