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 1 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 1 f (x) = 0 Calculating 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 f(x) = (a a1) (a a2) .. (a an)

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