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.

#Calculus

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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 - 5 years, 2 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.

Anirudh Chandramouli - 5 years, 2 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.

Mark Hennings - 5 years, 2 months ago

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

Anirudh Chandramouli - 5 years, 2 months ago

La solucion es la siguiente

Carlos Suarez - 5 years, 2 months ago

si señor, ¿podría explicar?

Anirudh Chandramouli - 5 years, 2 months ago

Hola tienes un email para enviarte la solucion, saludos

Carlos Suarez - 5 years, 2 months ago

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

Anirudh Chandramouli - 5 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$