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

##### Solution :-

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

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

(a1 – a1) (a1 – a2)…..(a– an) = 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 – an) = 0

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

Answered by Abhisek | 1 year ago

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