Last updated at Aug. 13, 2021 by Teachoo

Transcript

Example 6 Prove that the identity function on real numbers given by f (x) = x is continuous at every real number.Given π(π₯)=π₯ To check continuity of π(π₯), We check itβs if it is continuous at any point x = c Let c be any real number f is continuous at π₯ =π if (π₯π’π¦)β¬(π±βπ) π(π)=π(π) (π₯π’π¦)β¬(π±βπ) π(π) "= " limβ¬(xβπ) " " π₯ = π π(π) = π Since, L.H.S = R.H.S β΄ Function is continuous at x = c Thus, we can write that f is continuous for x = c , where c βπ β΄ f is continuous for every real number.

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Chapter 5 Class 12 Continuity and Differentiability (Term 1)

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About the Author

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.