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Funny Question on Calculus

Hello everyone. Today in class, my math teacher and me had a very long drawn debate about this question and were confused about how to solve the question. I have attached an image of the question. My doubt is whether the question is sensible asking us to find n after giving us a limit with n tending to 0. Also natural numbers don't tend to 0. Please help me out. I would appreciate it if anyone could post a solution or suggest some possible alteration to the question to obtain the correct answer. Thank you.

Note by Anirudh Chandramouli
1 year, 7 months ago

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Since \(b = a^n + \tfrac{1}{n a^{n-2}}\), perhaps the question wanted you to take the limit as \(a \to 0\). This gives a limit of \(\tfrac12\) when \(n=2\).

Mark Hennings - 1 year, 7 months ago

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Yes even we assumed that. But can we solve the question assuming the question to be right? Thank you for posting a solution.

Anirudh Chandramouli - 1 year, 7 months ago

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Even if you could let an integer \(n\) tend to 0, how would you expect to evaluate \(n\) by letting it tend to \(0\)?

You can (with the appropriate topology) let \(n\) tend to 0, but this amounts to setting \(n\) equal to 0, and \(b\) then does not exist for positive \(a\).

The question must be incorrectly stated.

Mark Hennings - 1 year, 7 months ago

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@Mark Hennings Yes that seems very logical. I understood now. Thank you once again.

Anirudh Chandramouli - 1 year, 7 months ago

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La solucion es la siguiente

Carlos Suarez - 1 year, 7 months ago

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si señor, ¿podría explicar?

Anirudh Chandramouli - 1 year, 7 months ago

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Hola tienes un email para enviarte la solucion, saludos

Carlos Suarez - 1 year, 7 months ago

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@Carlos Suarez si senor. anirudhvan@gmail.com gracias.

Anirudh Chandramouli - 1 year, 7 months ago

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