Example 7 - Is f(x) = |x| a continuous function - Class 12 - Checking continuity using LHL and RHL

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Example 7 Is the function defined by f (x) = |x|, a continuous function? = = <0 0 Checking continuity Case 1: At x = 0 f is continuous at x = 0 if, L.H.L = R.H.L = 0 i.e. lim x 0 = lim x 0 + = 0 & 0 = 0 Hence L.H.L = R.H.L = 0 f( ) is continuous at x = 0 Case 2 At x = c , c < 0 = is continuous at x = c if lim x = Hence lim x = therefore f is continuous at x = c (c < 0) f is continuous for all real number less then 0. Case 3 At x = c , c > 0 = is continuous at x = c if lim x = Hence lim x = f is continuous at x = c (c > 0) f is continuous for all real number greater then 0. Thus f is continuous for all real number

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.