# 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
5 years, 4 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 $n=2$.

- 5 years, 3 months ago

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

- 5 years, 3 months ago

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.

- 5 years, 3 months ago

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

- 5 years, 3 months ago

La solucion es la siguiente

- 5 years, 3 months ago

si señor, ¿podría explicar?

- 5 years, 3 months ago

Hola tienes un email para enviarte la solucion, saludos

- 5 years, 3 months ago

si senor. anirudhvan@gmail.com gracias.

- 5 years, 3 months ago