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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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Example 14 Show that every polynomial function is continuousLet 𝒇(𝒙)=𝒂_𝟎+𝒂_𝟏 𝒙+𝒂_𝟏 𝒙^𝟐+ … +𝒂_𝒏 𝒙^𝒏 𝑛∈𝒁 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 𝑥 = 𝑐 if (𝐥𝐢𝐦)┬(𝐱→𝒄) 𝒇(𝒙)= 𝒇(𝒄) L.H.S (𝐥𝐢𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = lim┬(x→𝑐) " " (𝑎_0+𝑎_1 𝑥+ … +𝑎_𝑛 𝑥^𝑛 ) Putting x = c = 𝑎_0+𝑎_1 𝑐+ … +𝑎_𝑛 𝑐^𝑛 R.H.S 𝒇(𝒄) = 𝑎_0+𝑎_1 𝑐+ … +𝑎_𝑛 𝑐^𝑛 Since, L.H.S = R.H.S ∴ Function is continuous at x = c Thus, we can write that f is continuous for all 𝒙 ∈𝐑 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.