Normally yes, but this one called a student asking for help dumb for not being able to answer an easy question, which has set me against him thoroughly.

Reply 1984

TeeEm

19

Original post by Zacken

Right, I've brought you up in the moderation team.

lol

Reply 1985

16Characters....

13

To add, doesn't it diverge for

n \leq 0

which I do not think has been mentioned yet.

If you want some integrals, try:

\displaystyle \int_0^1 \displaystyle \int_0^1 \frac{ dx dy}{1 - xy}

\displaystyle \int_0^1 \displaystyle \int_0^1 \frac{ dx dy} {1 - x^2 y^2 }

Reply 1986

GeologyMaths

2

Original post by studentro

That's incorrect, I'm afraid. Zacken got the correct answer.

I cant proof it is correct

Reply 1987

GeologyMaths

2

Original post by 16Characters....

To add, doesn't it diverge for

n \leq 0

which I do not think has been mentioned yet.

If you want some integrals, try:

\displaystyle \int_0^1 \displaystyle \int_0^1 \frac{ dx dy}{1 - xy}

\displaystyle \int_0^1 \displaystyle \int_0^1 \frac{ dx dy} {1 - x^2 y^2 }

Are you referring to space or me specifically?

Reply 1988

testing1234568

12

Original post by 16Characters....

To add, doesn't it diverge for

n \leq 0

which I do not think has been mentioned yet.

Yeah, that's correct.
(I had assumed n was a positive integer for some reason!)

Reply 1989

testing1234568

12

Original post by GeologyMaths

I cant proof it is correct

I worked it out to be

\frac{1}{2} (\frac{\pi}{n})^{\frac{1}{2}}

. I've checked it in Wolfram and it's correct. You're out by a factor of two, so you've probably only made a small slip up somewhere.

Reply 1990

username1162972

18

Original post by studentro

I worked it out to be

\frac{1}{2} (\frac{\pi}{n})^{\frac{1}{2}}

. I've checked it in Wolfram and it's correct. You're out by a factor of two, so you've probably only made a small slip up somewhere.

Show us mate

Posted from TSR Mobile

Original post by physicsmaths

Show us mate

I used pretty much exactly the same method as Geology, but didn't make the mistake with the limits that he did (pointed out below).

Original post by GeologyMaths

4I^2 = 4 \displaystyle \int_{0}^{\infty} \displaystyle \int_{0}^{\infty} e^{-(x^2 + y^2)} dx dy [br]= \displaystyle \int_{-\infty}^{\infty} \displaystyle \int_{-\infty}^{\infty} e^{-(x^2 + y^2)} dx dy [br]= \displaystyle \int_{0}^{2 \pi} \displaystyle \int_{0}^{\infty} r e^{-nr^2} dr d \theta = \frac{\pi}{n}[br]

(edited 8 years ago)

Reply 1993

GeologyMaths

2

Original post by studentro

I used pretty much exactly the same method as Geology, but didn't make the mistake with the limits that he did (pointed out below).

\displaystyle \int_{0}^{2 \pi} \displaystyle \int_{0}^{\infty} r e^{-nr^2} dr d \theta = \displaystyle \int_{-\infty}^{\infty} \displaystyle \int_{-\infty}^{\infty} e^{-(x^2 + y^2)} dx dy = 2 \displaystyle \int_{0}^{\infty} \displaystyle \int_{0}^{\infty} e^{-(x^2 + y^2)} dx dy

Thanks mate

Reply 1994

testing1234568

12

Original post by GeologyMaths

Thanks mate

No worries! Easy mistake to make :smile:

Edit: I made a mistake while texing it up myself! Should be a 4 rather than a 2.

(edited 8 years ago)

Reply 1995

niallbc

2

What are the biggest tips you could give me for starting STEP prep?r

Reply 1996

to4ka

3

Original post by Mihael_Keehl

SHould it not be less than and equal to?

No as it's proof by contradiction.

Posted from TSR Mobile

Reply 1997

Zacken

22

Original post by niallbc

What are the biggest tips you could give me for starting STEP prep?r

Finish C4 if you haven't, then choose one of:

(i) go through Siklos's booklet.

(ii) go through step correspondence assignments

(iii) jump straight into past papers (my personal favourite).

Reply 1998

shamika

OP

16

All

As we're approaching the date where Cambridge sends out it offer decisions, we should also be entering into the phase where STEP prep starts in earnest. Please can I ask everyone to keep a few basic things in mind?

- It can be daunting for those less confident to see lots of uni maths / complicated questions of the type which aren't on STEP. Every year people are put off posting because they are "intimidated" by some of the regular posters. I know no one goes out of their way to show off and intimidate, but there are other more relevant threads for some of the recent discussions.

Try The Proof is Trivial or threads like the hard integral thread / the hard sum/products thread where you'll be encouraged and challenged to solve these types of problems.

- Please remember that this thread is to help you prepare: no one should give out full solutions and people are encouraged to help each other out to give hints.

- Be patient if your post doesn't get answered straight away. People like me are unpaid volunteers (I'm writing this whilst talking to my boss :tongue:

) so we can't be constantly be on TSR :biggrin:

Hopefully lots of you will see this and we can get you through the exams. Good luck all for offers and see you all starting in the next week or so :biggrin:

(Really, you might as well start now. If you're after an easier paper to start with, I recommend STEP I 1994 but the style is slightly different to more recent papers.)

Reply 1999

Zacken

22

Original post by shamika

- Be patient if your post doesn't get answered straight away. People like me are unpaid volunteers (I'm writing this whilst talking to my boss :tongue:

) so we can't be constantly be on TSR :biggrin:

Big LOL!

(Really, you might as well start now. If you're after an easier paper to start with, I recommend STEP I 1994 but the style is slightly different to more recent papers.)

For those starting with STEP III: STEP III 1997 is an excellent paper to get started, analogous to STEP I 1994 for STEP I beginners.

Good luck and I'm looking forward to doing some maths with you all! :biggrin:

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