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

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

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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 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.