Let a1- a2- - - an be fixed real numbers and define a function f x - x-a1 x-a2 - x-an What is limx- a1f x - For some a- a1- a2- - an- compute limx- af x -

We have f ( x )= ( x a_1 )(x a_2)..... ( x a_n ) lim_x→ a_1f ( x )=lim_x→ a_3 [ ( x a_1 ) ( x a_2 )··· ( x a_n ) ] = nbsp; [ lim_x→ a_1 ( x ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

Let a1, a2,...

Question

Let $a_{1}, a_{2}, \cdot \cdot \cdot \cdot, a_{n}$ 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 $a \neq a_{1}, a_{2} \cdot \cdot \cdot, a_{n},$ compute $lim x \to a f (x) \cdot$

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Solution

We have $f (x) = (x - a_{1}) (x - a_{2}) . . . . . (x - a_{n})$
$lim x \to a_{1} f (x) = lim x \to a_{3} [(x - a_{1}) (x - a_{2}) \cdot \cdot \cdot (x - a_{n})]$
= $[lim x \to a_{1} (x - a_{1})] [lim x \to a_{1} (x - a_{2})]$ ... $[lim x \to a_{1} (x - a_{n})]$
= $(a_{1} - a) (a_{1} - a_{2})$ ... $(a_{1} - a_{n}) = 0$
$∴ lim x \to a_{1} f (x) = 0$
Now $lim x \to a f (x) = lim x \to a [(x - a_{1}) (x - a_{2}) \cdot \cdot \cdot (x - a_{n})]$
= $[lim x \to a (x - a_{1})] [lim x \to a (x - a_{2})]$ ... $[lim x \to a (x - a_{n})]$
= $(a - a_{1}) (a - a_{2})$ ... $(a - a_{n})$
$∴ lim x \to a f (x) = (a - a_{1}) (a - a_{2})$ ... $(a - a_{n})$

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Let a1,a2,⋅⋅⋅⋅,an be fixed real numbers and define a functionf(x)=(x−a1)(x−a2).....(x−an)What is limx→a1f(x)? For some a≠a1,a2⋅⋅⋅,an, compute limx→af(x)⋅

Let $a_{1}, a_{2}, \cdot \cdot \cdot \cdot, a_{n}$ be fixed real numbers and define a function
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