Let a 1- a 2- - a n be fixed real numbers and define a function f x - x - a 1 x - a 2 - x - a n - What is lim x - a 1 f x -For some a- a 1- a 2- a n- compute lim v f x -

Here f(x) = (x a_1)(x a_2) ...(x a_n) Now x → a_1lim f(x) = x → a_1lim (x a_1)(x a_2) ...(x a_n) = (a_1 a_1) (a_1 a_2)...(a_1 a_n) = 0 × (a a_1) (a a_2) ...(a_1 ...

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Byju's Answer

Standard XI

Mathematics

Algebra of Limits

Let a 1, a 2,...

Question

Let $a_{1}$ , $a_{2}$ , ..., $a_{n}$ be fixed real numbers and define a function f(x) = $(x - a_{1}) (x - a_{2}) . . . (x - a_{n})$ . What is $lim x \to a_{1}$ f(x)?
For some a $\neq a_{1}, a_{2} . . . a_{n}$ , compute $lim x \to a$ f(x).

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Solution

Here f(x) = $(x - a_{1}) (x - a_{2}) . . . (x - a_{n})$

Now $lim x \to a_{1} f (x) = lim x \to a_{1} (x - a_{1}) (x - a_{2}) . . . (x - a_{n})$

= $(a_{1} - a_{1}) (a_{1} - a_{2}) . . . (a_{1} - a_{n})$

= 0 $\times (a - a_{1}) (a - a_{2})$ ... $(a_{1} - a_{n})$ = 0.

Also $lim x \to a f (x) = lim x \to a (x - a_{1}) (x - a_{2}) . . . (x - a_{n})$

= $(a - a_{1}) (a - a_{2}) . . . (a - a_{n})$

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Let a1, a2, ..., an be fixed real numbers and define a function f(x) = (x−a1)(x−a2)...(x−an). What is limx→a1 f(x)? For some a ≠a1,a2...an, compute limx→a f(x).

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