Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12



  1. Chapter 5 Class 12 Continuity and Differentiability
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Ex 5.1, 31 Show that the function defined by ๐‘“(๐‘ฅ)=cosโก(๐‘ฅ^2 ) is a continuous function. ๐‘“(๐‘ฅ) = cosโก(๐‘ฅ^2 ) Let ๐‘”(๐‘ฅ) = cosโก๐‘ฅ & โ„Ž(๐‘ฅ) = ๐‘ฅ^2 ๐‘”๐‘œโ„Ž(๐‘ฅ) = g(โ„Ž(๐‘ฅ)) = ๐‘”(๐‘ฅ^2 ) = cosโก(๐‘ฅ^2 ) = ๐‘“(๐‘ฅ) So we can write ๐‘“(๐‘ฅ) = ๐‘”๐‘œโ„Ž Here ๐‘”(๐‘ฅ) = cosโก๐‘ฅ is continuous & โ„Ž(๐‘ฅ) = ๐‘ฅ^2 is continuous as it is a polynomial . We now that if two functions ๐‘“(๐‘ฅ) & โ„Ž(๐‘ฅ) both continuous then their composition ๐‘”๐‘œโ„Ž(๐‘ฅ) is continuous โˆด Hence (๐‘”๐‘œโ„Ž) (๐‘ฅ) is continuous Thus, ๐’‡(๐’™) 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.