Let a 1- a 2- - a n be fixed real numbers such that f x - x - a 1 x - a 2 - - x - a n What is lim x - a 1 f x - For - a 1- a 2- - a n computelim x - a fx

Lim_x → a_1 f(x) ⇒ (x a_1)(x a_2)....(x a_n) [Putting lim it x → a_1] ⇒ (a_1 a_1)(a_1 a_2)....(a_1 a_n) ⇒ 0 And, lim_x → af(x) ⇒ lim_x → a(x a_1)(x a_2)...( ...

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Byju's Answer

Standard XII

Mathematics

Limit

Let a 1, a 2,...

Question

Let $a_{1}, a_{2}, . . . . ., a_{n}$ be fixed real numbers such that $f (x) = (x - a_{1}) (x - a_{2}) . . . . (x - a_{n})$ What is $l i m_{x \to a_{1}}$ f(x)? For $a \neq a_{1}, a_{2}, . . . ., a_{n}$ compute $l i m_{x \to a} f (x) .$

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Solution

$l i m_{x \to a_{1}} f (x)$ \

$\Rightarrow (x - a_{1}) (x - a_{2}) . . . . (x - a_{n})$

[Putting lim it $x \to a_{1}]$

$\Rightarrow (a_{1} - a_{1}) (a_{1} - a_{2}) . . . . (a_{1} - a_{n})$

$\Rightarrow 0$

And, $l i m_{x \to a} f (x)$

$\Rightarrow l i m_{x \to a} (x - a_{1}) (x - a_{2}) . . . (x - a_{n})$

[Putting lim it $x \to a]$

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

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Let a1,a2,.....,an be fixed real numbers such that f(x)=(x−a1)(x−a2)....(x−an) What is limx→a1 f(x)? For a≠a1,a2,....,an compute limx→af(x).

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