Example 9 - Discuss continuity of f(x) = 1/x - Chapter 5

Example 9 - Chapter 5 Class 12 Continuity and Differentiability - Part 2
Example 9 - Chapter 5 Class 12 Continuity and Differentiability - Part 3

  1. Chapter 5 Class 12 Continuity and Differentiability (Term 1)
  2. Serial order wise

Transcript

Example 9 Discuss the continuity of the function f defined by 𝑓 (π‘₯) = 1/π‘₯ , π‘₯ β‰  0. Given 𝑓 (π‘₯) = 1/π‘₯ At 𝒙 = 𝟎 𝑓 (0) = 1/0 = ∞ Hence, 𝑓(π‘₯) is not defined at 𝒙=𝟎 By definition, 𝑓 (π‘₯) = 1/π‘₯ , π‘₯ β‰  0. So, we check for continuity at all points except 0. Let c be any real number except 0. f is continuous at π‘₯ =𝑐 if , (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙)=𝒇(𝒄) Since, L.H.S = R.H.S ∴ Function is continuous at x = c (Except 0) (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = lim┬(x→𝑐) 1/π‘₯ Putting π‘₯ =𝑐 = 1/𝑐 𝒇(𝒄) =1/𝑐 " " Thus, we can write that f is continuous for all 𝒙 βˆˆπ‘βˆ’{𝟎} Thus, we can write that f is continuous for all 𝒙 βˆˆπ‘βˆ’{𝟎}

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.