Turn on thread page Beta
 You are Here: Home >< Maths

# 0 divided by 0? watch

1. Hi,
I've recently got this question:

Let be the function
Compute .You may use l'Hôpital's rule provided that you can justify why you can apply it.

Now if i compute f(0), i.e. subsitute x in the formula for 0, as the question asks, it just simplifies to . This, however is undefined. As far as l'Hôpital's rule goes, as far as i was aware, it deals with limits, rather than actual values.

This makes me believe that there's a huge typo in the question, and that it wants me to evaluate the limit as x tends to 0. Is there any other way of interpreting this question that I can't see?
Help would be appreciated, this is the last piece of coursework i've got before the holidays and I'd love to get it out of the way ASAP.

Cheers.
2. black hole / Maths Error 2

the choice is yours
3. The question per se doesn't make sense unless it's part of a Limits exercise. I suspect it wants you to find f(x) as x -> 0.
4. (Original post by immense010)
Hi,
I've recently got this question:

Let be the function
Compute .You may use l'Hôpital's rule provided that you can justify why you can apply it.

Cheers.

Use the taylor expansion of the exponential term.

Boom
5. (Original post by MillerTraub)
Use the taylor expansion of the exponential term.

Boom
Oh yeah, didn't notice that. Only problem is the Taylor series expansion is infinite, so although it will cancel out the other 3 terms in the numerator, I'll still be left with an infinite series, with each term containing x to a certain power, so when I try substituting in x=0 it'll still give me 0/0

I got this homework for my analysis module, so I need to give an exact answer to the question, and so I can't just use the Taylor expansion of order 2, as this would be an approximation. Although I do agree with you that it would behave as f(x)=0 sufficiently close to the origin.
6. (Original post by immense010)
Oh yeah, didn't notice that. Only problem is the Taylor series expansion is infinite, so although it will cancel out the other 3 terms in the numerator, I'll still be left with an infinite series, with each term containing x to a certain power, so when I try substituting in x=0 it'll still give me 0/0

I got this homework for my analysis module, so I need to give an exact answer to the question, and so I can't just use the Taylor expansion of order 2, as this would be an approximation. Although I do agree with you that it would behave as f(x)=0 sufficiently close to the origin.
o'rly?
7. (Original post by immense010)
Oh yeah, didn't notice that. Only problem is the Taylor series expansion is infinite, so although it will cancel out the other 3 terms in the numerator, I'll still be left with an infinite series, with each term containing x to a certain power, so when I try substituting in x=0 it'll still give me 0/0

I got this homework for my analysis module, so I need to give an exact answer to the question, and so I can't just use the Taylor expansion of order 2, as this would be an approximation. Although I do agree with you that it would behave as f(x)=0 sufficiently close to the origin.
What is x^2 / x equal to when x=0?
8. aah lol ok i've spotted it. Thanks a lot ^^
9. The moral of the story here is:

If in doubt, the answer is always 1/6

Turn on thread page Beta
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 31, 2011
Today on TSR

### Uni league tables

Do they actually matter?

### University open days

• Staffordshire University
Everything except: Midwifery, Operating Department Practice, Paramedic Undergraduate
Sun, 21 Oct '18
• University of Exeter
Undergraduate Open Days - Exeter Campus Undergraduate
Wed, 24 Oct '18
• University of Bradford
Faculty of Health Studies Postgraduate
Wed, 24 Oct '18
Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE