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

Slide36.JPG

Slide37.JPG

  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

Transcript

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’ˆ(๐’™) = cosโก๐‘ฅ & ๐’‰(๐’™) = ๐‘ฅ^2 Now, ๐’ˆ๐’๐’‰(๐’™) = g(โ„Ž(๐‘ฅ)) = ๐‘”(๐‘ฅ^2 ) = cosโก(๐‘ฅ^2 ) = ๐’‡(๐’™) Hence, ๐‘“(๐‘ฅ) = ๐‘”๐‘œโ„Ž(๐‘ฅ) We know that ๐’ˆ(๐’™) = cosโก๐‘ฅ is continuous as cos x is always continuous & ๐’‰(๐’™) = ๐‘ฅ^2 is continuous as it is a polynomial Hence, ๐‘”(๐‘ฅ) & โ„Ž(๐‘ฅ) are both continuous . We know that If two function of ๐‘”(๐‘ฅ) & โ„Ž(๐‘ฅ) both continuous, then their composition ๐’ˆ๐’๐’‰(๐’™) is also continuous Hence, ๐’‡(๐’™) is continuous .

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.