Checking continuity at any point

Chapter 5 Class 12 Continuity and Differentiability
Concept wise

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Example 14 Show that every polynomial function is continuousLet π(π)=π_π+π_π π+π_π π^π+ β¦ +π_π π^π πβπ be a polynomial function Since Polynomial function is valid for every real number We prove continuity of Polynomial Function at any point c Let c be any real number f(x) is continuous at π₯ = π if (π₯π’π¦)β¬(π±βπ) π(π)= π(π) (π₯π’π¦)β¬(π±βπ) π(π) = limβ¬(xβπ) " " (π_0+π_1 π₯+ β¦ +π_π π₯^π ) Putting x = c = π_0+π_1 π+ β¦ +π_π π^π π(π) = π_0+π_1 π+ β¦ +π_π π^π Since, L.H.S = R.H.S β΄ Function is continuous at x = c Thus, we can write that f is continuous for all π βπ i.e. Every polynomial function is continuous.

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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.