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

Ex. 5.1,30 slide 2.jpg

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


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 .

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.