Ex 5.1 ,6 - Find all points of discontinuity of f(x) = {2x + 3 - Ex 5.1

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Ex 5.1, 6 Find all points of discontinuity of f, where f is defined by = 2 +3, 2 &2 3, >2 We have, = 2 +3, 2 &2 3, >2 Case 1 At =2 f is continuous at x = 2 if L.H.L = R.H.L = 2 i.e. lim x 2 = lim x 2 + = 2 Since, L.H.L R.H.L f is not continuous at x=2. Case 2 At = where c < 2 = 2 +3 f is continuous at x=c if lim x = Hence, lim x = f is continuous at x=c where c<2 Thus, f is continuous at all real number less than 2. Case 3 At = where c > 2 = 2 +3 f is continuous at x=c if lim x = Hence, lim x = f is continuous at x=c where c>2 f is continuous at all real number greater than 2 Hence, only x=2 is point is discontinuity. f is continuous at all real numbers except 2. Thus, f is continuous for R {2}.

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