WBJEE · Maths · Limits
\(\lim _{x \rightarrow \infty}\left\{x-\sqrt[n]{\left(x-a_1\right)\left(x-a_2\right) \ldots\left(x-a_n\right)}\right\}\) where \(a_1, a_2, \ldots, a_n\) are positive rational numbers. The limit
- A does not exist
- B is \(\frac{a_1+a_2+\ldots a_n}{n}\)
- C is \(\sqrt[n]{a_1 a_2 \ldots a_n}\)
- D is \(\frac{n}{a_1+a_2+\ldots+a_n}\)
Answer & Solution
Correct Answer
(B) is \(\frac{a_1+a_2+\ldots a_n}{n}\)
Step-by-step Solution
Detailed explanation
Hint: \(\operatorname{lt}_{x \rightarrow \infty}\left\{x-\sqrt[x]{\left(x-a_1\right)\left(x-a_2\right) \ldots\left(x-a_n\right)}\right\}\)…
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