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Byju's Answer

Standard X

Mathematics

Concept of Inequality

Let a1, a2, …...

Question

Let a₁, a₂, ..., a_n be fixed real numbers such that
f(x) = (x − a₁) (x − a₂) ... (x − a_n)
What is $\lim_{x \to a_{1}} f (x) ?$ For a ≠ a₁, a₂, ..., a_n. Compute $\lim_{x \to a} f (x) .$

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Solution

$f (x) = (x - a_{1}) (x - a_{2}) . . . (x - a_{n}) \lim_{x \to a_{1}} f (x) = \lim_{x \to a_{1}} [(x - a_{1}) (x - a_{2}) . . . (x - a_{n})] = (a_{1} - a_{1}) (a_{1} - a_{2}) . . . (a_{1} - a_{n}) = 0 \lim_{x \to a} f (x) = \lim_{x \to a} (x - a_{1}) (x - a_{2}) . . . (x - a_{n}) = (a - a_{1}) (a - a_{2}) . . . (a - a_{n})$

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