Check sibling questions

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

This video is only available for Teachoo black users

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

This video is only available for Teachoo black users

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

Β 

Solve all your doubts with Teachoo Black (new monthly pack available now!)


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

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.