Ex 5.1, 9 - Find all points of discontinuity - Chapter 5 Class 12 - Ex 5.1

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Ex 5.1, 9 Find all points of discontinuity of f, where f is defined by = , <0 & 1 , 0 Given = , <0 & 1 , 0 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 = 1 Thus, L.H.L = R.H.L = f(0) f is continuous at =0 Case 2 Let x = c (where c > 0) = 1 f is continuous at x = c if lim x = ( ) Thus lim x = ( ) f is continuous for =( greater than 0). f is at continuous for all real numbers greater than 0. Case 3 Let x = c (where c < 0) = = = 1 f is continuous at x = c if lim x = ( ) Thus , lim x = ( ) f is continuous for = ( c is less than 0 ) f is continuous for all real numbers less than 0. Thus, f is continuous for x R {0} Hence f(x) is continuous at all points f is continuous

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