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Ex 13.1, 29 - Let a1, a2, .. , an be fixed real numbers - Ex 13.1

Ex 13.1, 29 - Chapter 13 Class 11 Limits and Derivatives - Part 2

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Ex 13.1, 29 Let a1, a2,….., an be fixed real numbers and define a function f(x) = (x – a1) (x – a2)…. (x – an) What is lim┬(x→a"1" ) f(x)? For some a ≠ a1, a2…… an, compute lim┬(x→a) f(x). f(x) = (x – a1) (x – a2) …….(x – an) Calculating (𝐥𝐢𝐦)┬(𝐱→𝐚"1" ) f(x) lim┬(x→a"1" ) f(x) = lim┬(x→a"1" ) (x – a1) (x – a2)….. (x – an) Putting x = a1 = (a1 – a1) (a1 – a2) …..(a1 – an) = 0 × (a1 – a2) …… (a1 – an) = 0 Hence, (𝐥𝐢𝐦)┬(𝐱→𝐚"1" ) f (x) = 0 Calculating (𝐥𝐢𝐦)┬(𝐱→𝐚) f(x) lim┬(x→a) f(x) = lim┬(x→a) (x – a1) (x – a2) …….(x – an) Putting x = a = (a – a1) (a – a2) …… (a – an) Hence (𝐥𝐢𝐦)┬(𝐱→𝐚) f(x) = (a – a1) (a – a2) ….. (a – an)

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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.