Ex 5.1, 31 - Show that f(x) = cos(x2) is continuous - Ex 5.1

Slide40.JPG

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

Transcript

Ex 5.1, 31 Show that the function defined by 𝑓 𝑥﷯= cos﷮ 𝑥﷮2﷯﷯﷯ is a continuous function. 𝑓(𝑥) = cos﷮ 𝑥﷮2﷯﷯﷯ Let 𝑔(𝑥) = cos﷮𝑥﷯ & ℎ 𝑥﷯ = 𝑥﷮2﷯ 𝑔𝑜ℎ 𝑥﷯ = g ℎ 𝑥﷯﷯ = 𝑔 𝑥﷮2﷯﷯ = cos﷮ 𝑥﷮2﷯﷯﷯ = 𝑓 𝑥﷯ So we can write 𝑓 𝑥﷯ = 𝑔 𝑜 ℎ Here 𝑔 𝑥﷯ = sin﷮𝑥﷯ is continuous & ℎ 𝑥﷯ = 𝑥﷮2﷯ is continuous being a polynomial . We now that if two function 𝑓 𝑥﷯ & ℎ 𝑥﷯ both continuous then their composition 𝑔𝑜ℎ 𝑥﷯ is continuous ∴ Hence 𝑔 𝑜 ℎ﷯ 𝑥﷯ is continuous Thus, 𝒇 𝒙﷯ is continuous .

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.