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

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

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

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Davneet Singh

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.