Ex 5.1, 31 - Ex 5.1

Ex 5.1, 31 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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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 Now, 𝒈𝒐𝒉(𝒙) = g(ℎ(𝑥)) = 𝑔(𝑥^2 ) = cos⁡(𝑥^2 ) = 𝒇(𝒙) Hence, 𝑓(𝑥) = 𝑔𝑜ℎ(𝑥) We know that 𝒈(𝒙) = cos⁡𝑥 is continuous as cos x is always continuous & 𝒉(𝒙) = 𝑥^2 is continuous as it is a polynomial Hence, 𝑔(𝑥) & ℎ(𝑥) are both continuous . We know that If two function of 𝑔(𝑥) & ℎ(𝑥) both continuous, then their composition 𝒈𝒐𝒉(𝒙) is also continuous Hence, 𝒇(𝒙) is continuous .

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.