Check sibling questions

Example 6 - Examples

Example 6 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

This video is only available for Teachoo black users

Introducing your new favourite teacher - Teachoo Black, at only β‚Ή83 per month


Transcript

Example 6 Prove that the identity function on real numbers given by f (x) = x is continuous at every real number.Given 𝑓(π‘₯)=π‘₯ To check continuity of 𝑓(π‘₯), We check it’s if it is continuous at any point x = c Let c be any real number f is continuous at π‘₯ =𝑐 if (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙)=𝒇(𝒄) (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙) "= " lim┬(x→𝑐) " " π‘₯ = 𝑐 𝒇(𝒄) = 𝑐 Since, L.H.S = R.H.S ∴ Function is continuous at x = c Thus, we can write that f is continuous for x = c , where c βˆˆπ‘ ∴ f is continuous for every real number.

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.