Let a1, a2,………an be fixed real numbers and define a function f (x) = (x – a1) (x – a2) ……. (x – an).

Question

Let a1, a2,………an be fixed real numbers and define a function f (x) = (x – a1) (x – a2) ……. (x – an).

Let a₁, a_2,………a_n be fixed real numbers and define a function f (x) = (x – a₁) (x – a₂) ……. (x – a_n).What is \( \lim\limits_{x \to a_1}f(x)\). For some \( a\neq a_1,a_2,....a_n\)

Compute \( \lim\limits_{x \to a}f(x)\)

Asked by Pragya Singh | 1 year ago | 100

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Class 11 Maths Limits and Derivatives Add Answer

1 Answer

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Accepted Answer

Solution :-

The given function is f(x) = (x – a₁) (x – a₂)…..(x – a_n)

\( \lim\limits_{x \to a_1}[(x-a_1)(x-a_2)....(x-a_n)]\)

(a₁ – a₁) (a₁ – a₂)…..(a₁– a_n) = 0

\( \lim\limits_{x \to a_1}f(x)=0\)

\( \lim\limits_{x \to a}f(x)= \lim\limits_{x \to a} [(x-a_1)(x-a_2)....(x-a_n)]\)

(a₁ – a₁) (a – a₂)…..(a– a_n) = 0

\( \lim\limits_{x \to a}f(x)=(a – a_1) (a – a_2)…..(a – a_n) = 0\)

Answered by Abhisek | 1 year ago