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

Ex 5.1, 21 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

Ex 5.1, 21 - Chapter 5 Class 12 Continuity and Differentiability - Part 3

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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 ∴ 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.