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

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  1. Chapter 13 Class 11 Limits and Derivatives
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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→a1﷯ 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→𝐚1﷯ f(x) lim﷮x→a1﷯ f(x) = lim﷮x→a1﷯ (x – a1) (x – a2)….. (x – an) Putting x = a1 = (a1 – a1) (a1 – a2) …..(a1 – an) = 0 × (a1 – a2) …… (a1 – an) = 0 Hence 𝐥𝐢𝐦﷮𝐱→𝐚1﷯ 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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