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

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

Transcript

Ex 5.1, 21 Discuss the continuity of the following functions: (a) 𝑓 (π‘₯) = sin⁑π‘₯+cos⁑π‘₯ 𝑓 (π‘₯) = sin⁑π‘₯+cos⁑π‘₯ Let 𝑝(π‘₯)=sin⁑π‘₯ & π‘ž(π‘₯)=cos⁑π‘₯" " We know that sin⁑π‘₯ & cos⁑π‘₯ both continuous function ∴ 𝒑(𝒙) & 𝒒(𝒙) is continuous at all real number By Algebra of continuous function If 𝑝(π‘₯)" & " π‘ž(π‘₯) are continuous for all real numbers then 𝑓(π‘₯)= 𝒑(𝒙)+𝒒(𝒙) is continuous for all real numbers ∴ 𝒇(𝒙) = sin⁑π‘₯+π‘π‘œπ‘ β‘π‘₯ continuous for all real numbers Ex 5.1, 21 Discuss the continuity of the following functions: (b) 𝑓(π‘₯) = sin⁑π‘₯ – cos⁑π‘₯ 𝑓(π‘₯)= sin⁑π‘₯ – cos⁑π‘₯ Let 𝑝(π‘₯)=sin⁑π‘₯ & π‘ž(π‘₯)=cos⁑π‘₯" " We know that sin⁑π‘₯ & cos⁑π‘₯ are both continuous function ∴ 𝒑(𝒙) & 𝒒(𝒙) is continuous at all real number By Algebra of continuous function If 𝑝(π‘₯)" & " π‘ž(π‘₯) are continuous for all real numbers then 𝑓(π‘₯)= 𝒑(𝒙)βˆ’π’’(𝒙) is continuous for all real numbers ∴ 𝒇(𝒙) = 𝑠𝑖𝑛⁑π‘₯βˆ’π‘π‘œπ‘ β‘π‘₯ is continuous for all real numbers Ex 5.1, 21 Discuss the continuity of the following functions: (c) 𝑓(π‘₯) = sin⁑π‘₯ . cos⁑π‘₯ 𝑓(π‘₯) = sin⁑π‘₯ . cos⁑π‘₯ Let 𝑝(π‘₯)=sin⁑π‘₯ & π‘ž(π‘₯)=cos⁑π‘₯" " We know that sin⁑π‘₯ & cos⁑π‘₯ are both continuous functions ∴ 𝒑(𝒙) & 𝒒(𝒙) is continuous at all real numbers By Algebra of continuous function If 𝑝(π‘₯)" & " π‘ž(π‘₯) are continuous for all real numbers then 𝑓(π‘₯)= 𝒑(𝒙) . 𝒒(𝒙) is continuous for all real numbers ∴ 𝒇(𝒙) = 𝑠𝑖𝑛⁑π‘₯.π‘π‘œπ‘ β‘π‘₯ continuous for all real numbers

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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.