Example 6 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at August 11, 2026 by Teachoo
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Chapter 5 Class 12 Continuity and Differentiability
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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) L.H.S (π₯π’π¦)β¬(π±βπ) π(π) "= " limβ¬(xβπ) " " π₯ = π R.H.S 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.
