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Ex 5.1, 21 - Discuss continuity of (a) f(x) = sin⁑ x + cos⁑ x - Ex 5.1

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  1. Chapter 5 Class 12 Continuity and Differentiability
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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 β‡’ 𝑝(π‘₯) & π‘ž(π‘₯) 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(π‘₯)+π‘ž(π‘₯) is continuous for all real numbers ∴ 𝒇(𝒙) = 𝐬𝐒𝐧⁑𝒙+𝒄𝒐𝒔⁑𝒙 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 β‡’ 𝑝(π‘₯) & π‘ž(π‘₯) 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(π‘₯)βˆ’π‘ž(π‘₯) is continuous for all real numbers ∴ 𝒇(𝒙) = π’”π’Šπ’β‘π’™βˆ’π’„π’π’”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 β‡’ 𝑝(π‘₯) & π‘ž(π‘₯) 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(π‘₯) . π‘ž(π‘₯) is continuous for all real numbers ∴ 𝒇(𝒙) = π’”π’Šπ’β‘π’™.𝒄𝒐𝒔⁑𝒙 continuous for all real numbers

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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