Example 5 - Check the points where f(x) = k is continuous

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

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

Transcript

Example 5 Check the points where the constant function 𝑓 (π‘₯) = π‘˜ is continuous. Given 𝑓(π‘₯)=π‘˜ (where π‘˜ is any constant) To check continuity of 𝑓(π‘₯), We check it’s if it is continuous at any point x = c Let c be any real number f is continuous at π‘₯ =𝑐 if (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙)=𝒇(𝒄) (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙) "= " lim┬(x→𝑐) " " π‘˜ = π‘˜ 𝒇(𝒄) = π‘˜ Since, L.H.S = R.H.S ∴ Function is continuous at x = c Thus, we can write that f is continuous for x = c , where c βˆˆπ‘ ∴ f is continuous for every real number.

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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.