Let a1-a2- an be fixed real numbers and define a function fx-x-a1x-a2-x-an-What is lim x- a1fx- For some a- a1-a2- an- compute lim x- a fx-

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Standard XII

Mathematics

Summation by Sigma Method

Let a1,a2,....

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

$\begin{matrix} f (x) = (X - a_{1}) (X - a_{2}) . . . . . . . . . . (X - a_{n}) {lim}_{x \to a} f (x) = (a_{1} - a_{1}) (a_{1} - a_{2}) . . . . . . . . . . (a_{1} - a_{n}) 0. (a_{1} - a_{2}) . . . . . . . . . = 0 {lim}_{x \to a} f (x) = (a_{1} - a_{1}) (a_{1} - a_{2}) . . . . . . . . . . (a_{1} - a_{n}) = 0 \end{matrix}$

Hence, this is the answer.

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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→a1f(x)? For some a≠a1,a2,...,an, compute limx→af(x).

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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 $lim x \to a f (x)$ .