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Ex 5.1, 32 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Ex 5.1, 32 Show that the function defined by 𝑓 𝑥= cos𝑥 is a continuous function. 𝑓(𝑥) = cos𝑥 Let 𝑔(𝑥) = 𝑥 & ℎ 𝑥 = cos𝑥 𝑔𝑜ℎ 𝑥 = g ℎ 𝑥 = 𝑔 cos𝑥 = cos𝑥 = 𝑓 𝑥 Hence 𝑓 𝑥 = 𝑔𝑜ℎ 𝑥 We know that, h(x) = cos𝑥 is continuous & g (x) = 𝑥 is continuous as it is a modulus function We know that If two function 𝑔 𝑥 & ℎ 𝑥 both continuous then their composition is also continuous ∴ 𝑔𝑜ℎ 𝑥 is continuous Thus, 𝒇 𝒙 is continuous for all real values.
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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.