Ex 5.1, 16 - Chapter 5 Class 12 Continuity and Differentiability

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Ex 5.1, 16 Discuss the continuity of the function f, where f is defined by = &2, 1 2& , 1 1 2, >1 Case 1:- At x = 1 A function is continuous at x = 1 if L.H.L = R.H.L = 1 i.e. lim x 1 = lim x 1 + = 1 And 2 = 2 Thus L.H.L = R.H.L = 2 = 2 Hence is continuous at x = Case 1:- At x = 1 A function is continuous at x = 1 if A function is continuous at x = 1 if if L.H.L = R.H.L = 1 i.e. lim x 1 = lim x 1 + = 1 & 1 = 2 1 = 2 Thus L.H.L = R.H.L = 2 Hence is continuous at x = 1 Case 3:- For < 1 = 2 Thus, is a constant function . & Every constant function is continuous for all real number. Hence is continuous at < Case 4:- For >1 = 2 Thus, is a constant function . & Every constant function is continuous for all real number. Hence is continuous at > Case 5:- For 1 1 = 2 So, f(x) is a polynomial & Every polynomial is continuous. is continuous at < Thus, f(x) is continuous for all real numbers, i.e. f is continuous for all x R