You are Here: Home >< Maths

Limits Question Watch

1. Good afternoon folks,

I've been working few some problems sheets and have come a cropper with a question. Any help would be massively appreciated.

My attempt at this question led to me separating tanx into which gives us a common denominator of , so we have

This, however, led me down a bit of a dark alley, without a paddle, so to speak. I tried substituting the Maclaurin expansion in, which I couldn't simplify or evaluate.

Where should I go?
2. try L'hopital rule
3. (Original post by nigel_s)
Good afternoon folks,

I've been working few some problems sheets and have come a cropper with a question. Any help would be massively appreciated.

My attempt at this question led to me separating tanx into which gives us a common denominator of , so we have

This, however, led me down a bit of a dark alley, without a paddle, so to speak. I tried substituting the Maclaurin expansion in, which I couldn't simplify or evaluate.

Where should I go?
You can use l'Hôpital's rule on .
4. Aha! Of course! Many thanks.

I do have another question, I wonder if anyone could help with this one:

I really can't see where to go with this one. I tried taking the root x into the brackets, and then multiplying by to give but I still can't see how to solve and suspect I've taken another wrong turn.

Again, any help will be massively appreciated
5. (Original post by nigel_s)
Aha! Of course! Many thanks.

I do have another question, I wonder if anyone could help with this one:

I really can't see where to go with this one. I tried taking the root x into the brackets, and then multiplying by to give but I still can't see how to solve and suspect I've taken another wrong turn.

Again, any help will be massively appreciated
Why not multiply by instead? I don't know why you multiplied by what you did -- it looks like you half-expanded the bracket or something... but either way it was wrong
6. You've taken it into the brackets incorrectly. You should get

Try multiplying through by (on the top and bottom)
7. Okay have multiplied by

Giving me:

Can't see what to do next though?
8. (Original post by nigel_s)
Okay have multiplied by

Giving me:

Can't see what to do next though?
Divide top and bottom by , and then take the limit as .
9. Excellent, many thanks. Have solved both these problems now.

However, I have one final question (for tonight, at least).

What I did was to subsitute for

Which gave:

Which I calculate to be

What've I done wrong?
10. (Original post by nigel_s)
Excellent, many thanks. Have solved both these problems now.

However, I have one final question (for tonight, at least).

Start by using the identity and express the whole lot in terms of . Then do some simplification and it falls out.
11. (Original post by nuodai)
Start by using the identity and express the whole lot in terms of . Then do some simplification and it falls out.
Done - great, thanks very much for all your help

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: December 28, 2010
Today on TSR

Find out how.

Want £10K to start a business?

Discussions on TSR

• Latest
• See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

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

Chat with other maths applicants

Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• 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

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.