Ex 5.1, 25 - Examine continuity of f(x) = {sin x - cos x, -1 - Ex 5.1

Slide22.JPG
Slide23.JPG

  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
Ask Download

Transcript

Ex 5.1, 25 Examine the continuity of f, where f is defined by = sin , 0 & 1, =0 = sin , 0 & 1, =0 Case 1: At x = 0 f (x) is continuous at x = 0 if LHL = RHL = f(0) l x 0 = l x 0 = 0 And f(x) = sin x cos x f(0) = sin 0 cos 0 = 1 Hence, L H L = R H L = f(0) f (x) is continuous at x = 0 Case 2: For x 0 f(x) = sin x cos x Let p (x) = sinx & q (x) = cos x We know that, sin x & cos x are both continuous functions So, p(x) & q (x) is continuous at all real numbers By Algebra of continuous functions, If & both continuous for all real number , then f(x) = p(x) q(x) is continuous at all real numbers f(x) = sin x cos x is continuous for all real numbers. Hence, f(x) is continuous at all points

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.