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Last updated at Aug. 13, 2021 by Teachoo

Transcript

Ex 5.1, 31 Show that the function defined by ๐(๐ฅ)=cosโก(๐ฅ^2 ) is a continuous function.๐(๐ฅ) = cosโก(๐ฅ^2 ) Let ๐(๐) = cosโก๐ฅ & ๐(๐) = ๐ฅ^2 Now, ๐๐๐(๐) = g(โ(๐ฅ)) = ๐(๐ฅ^2 ) = cosโก(๐ฅ^2 ) = ๐(๐) Hence, ๐(๐ฅ) = ๐๐โ(๐ฅ) We know that ๐(๐) = cosโก๐ฅ is continuous as cos x is always continuous & ๐(๐) = ๐ฅ^2 is continuous as it is a polynomial Hence, ๐(๐ฅ) & โ(๐ฅ) are both continuous . We know that If two function of ๐(๐ฅ) & โ(๐ฅ) both continuous, then their composition ๐๐๐(๐) is also continuous Hence, ๐(๐) is continuous .

Ex 5.1

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Ex 5.1, 3 (a)

Ex 5.1, 3 (b)

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Ex 5.1, 31 You are here

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.