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# The Proof is Trivial! watch

1. (Original post by henpen)
I'm not quite sure what you mean, but

has finite area, despite having an asymptote.

Edit: Please be clearer, I don't see how the above is not a counterexample to your claim.
probably because you didnt read his last sentence...
2. Problem 424 */**

Find the integral of ln(cosx) between x=pi/2 and x=0
3. Problem 424 */**

The sum of the base-10 logarithms of the divisors of 10^N is 729 792 for some natural number N
.What is the value of N ?

Edit: There was a mistake
4. (Original post by IceKidd)
Problem 424 */**

Find the integral of ln(cosx) between x=pi/2 and x=0
This is going to look dreadful, although I have put in some effort putting in arrows and stuff

Solution 424

Building on what we've seen previously when the boundaries are pi/2 and 0 and the interchangeability therein of sin(x) and cos(x)..

5. (Original post by nahomyemane778)
Problem 424 */**

The sum of the base-10 logarithms of the divisors of 10^N is 729 for some natural number N
.What is the value of N ?

I think you mean .
6. Thanks for that felix, I was wondering where I went wrong with N = 1/3 (-2+(19684-81 (59055)^(1/2))^(1/3)+(19684+81 (59055)^(1/2))^(1/3))
7. (Original post by Llewellyn)
Thanks for that felix, I was wondering where I went wrong with N = 1/3 (-2+(19684-81 (59055)^(1/2))^(1/3)+(19684+81 (59055)^(1/2))^(1/3))
Hows durham? Are u top of ur class
8. (Original post by Felix Felicis)
I think you mean .
How on earth did you possibly know? Have you see this question before?
Nice to see good old feynman back for christmas
9. (Original post by Llewellyn)
Thanks for that felix, I was wondering where I went wrong with N = 1/3 (-2+(19684-81 (59055)^(1/2))^(1/3)+(19684+81 (59055)^(1/2))^(1/3))

(Original post by nahomyemane778)
How on earth did you possibly know? Have you see this question before?
Nice to see good old feynman back for christmas
Nope - I got to the stage where I had an equation with no integer solutions for the value you gave (), checked my working over and realised there's a mistake in the question and 792 just so happened to give a nice value for N.

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10. (Original post by Felix Felicis)

Nope - I got to the stage where I had an equation with no integer solutions for the value you gave (), checked my working over and realised there's a mistake in the question and 792 just so happened to give a nice value for N.

Posted from TSR Mobile
Ahh ok then- well done- I've amended the OP so you can post the solution now.
11. N = 11 using the Bertrand-Chebyshev theorem.
12. (Original post by Zakee)
N = 11 using the Bertrand-Chebyshev theorem.
err... what? How does that solve the problem?

13. (Original post by nahomyemane778)
err... what? How does that solve the problem?

Proof:

By concavity of the right-hand side as a function of n, the last inequality is necessarily verified on an interval. Since it holds true for and not , upper bound is the equating value which is:

The proof is trivial
14. (Original post by Zakee)
Proof:

By concavity of the right-hand side as a function of n, the last inequality is necessarily verified on an interval. Since it holds true for and not , upper bound is the equating value which is:

The proof is trivial
Well that's some pretty heavy machinery you've used- I dont understand at all to be honest. Is it university level?
15. (Original post by nahomyemane778)
Well that's some pretty heavy machinery you've used- I dont understand at all to be honest. Is it university level?
I'm currently in year 13, and I think it may be University level, I'm not sure. I heard from someone that it comes up in FP3 (A-level), but I haven't studied FP3 yet. I'm just extremely interested in Pure Mathematics and have a knack for problem-solving.
16. (Original post by Zakee)
Proof

The proof is trivial
What is that?
17. (Original post by Zakee)
I'm currently in year 13, and I think it may be University level, I'm not sure. I heard from someone that it comes up in FP3 (A-level), but I haven't studied FP3 yet.
It's most definitely university level (and quite specialist).
18. Problem 425*/**/***

Evaluate
19. I wonder if I am sober enough to do that LOTF...

Definitely not sober enough to latex it
20. (Original post by Lord of the Flies)
Problem 425*/**/***

Evaluate

Solution 425

Consider a trapezium with base 1, and two parallel sides of lengths 14 and 21. Its area is given by

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