Ex 5.1, 31
Last updated at May 29, 2018 by Teachoo
Transcript
Ex 5.1, 31 Show that the function defined by 𝑓 𝑥= cos 𝑥2 is a continuous function. 𝑓(𝑥) = cos 𝑥2 Let 𝑔(𝑥) = cos𝑥 & ℎ 𝑥 = 𝑥2 𝑔𝑜ℎ 𝑥 = g ℎ 𝑥 = 𝑔 𝑥2 = cos 𝑥2 = 𝑓 𝑥 So we can write 𝑓 𝑥 = 𝑔 𝑜 ℎ Here 𝑔 𝑥 = sin𝑥 is continuous & ℎ 𝑥 = 𝑥2 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.