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

Last updated at Jan. 3, 2020 by Teachoo

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

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(๐ฅ) = cosโก๐ฅ & โ(๐ฅ) = ๐ฅ^2 ๐๐โ(๐ฅ) = g(โ(๐ฅ)) = ๐(๐ฅ^2 ) = cosโก(๐ฅ^2 ) = ๐(๐ฅ) So we can write ๐(๐ฅ) = ๐๐โ Here ๐(๐ฅ) = cosโก๐ฅ is continuous & โ(๐ฅ) = ๐ฅ^2 is continuous as it is a polynomial . We now that if two functions ๐(๐ฅ) & โ(๐ฅ) both continuous then their composition ๐๐โ(๐ฅ) is continuous โด Hence (๐๐โ) (๐ฅ) is continuous Thus, ๐(๐) is continuous .

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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.