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#1 Re: This is Cool » n^2 » 2013-11-29 13:24:43
Thanks bobby 
I think the symmetry is pretty cool!
#2 This is Cool » n^2 » 2013-11-29 06:49:30
- Nils-Ake
- Replies: 8
I have just realized
#3 Re: Help Me ! » integration » 2009-03-12 04:07:32
The finite region is [0,4]:
Expand f(x):
Integrate:
edit: added graph
#4 Help Me ! » Taylor polynomial » 2008-11-27 14:12:12
- Nils-Ake
- Replies: 1
Hi. I'm doing something wrong here but I can't find out what it is.
Use Taylor's theorem to determine the degree of the Taylor polynomial for ln(1-x) required for the error in the approximation of ln(0.75) to be less than .001.
(I assume it is centered at a = 0)
Derivatives:
Taylor polynomial:
Where
------------------------------------------------------------------------
Now I evaluate the polynomial for x=0.25
At this point I plotted f^n+1 and saw that
So this should give me the answer
I get n>=3 but the book says n>=4. Where did I go wrong? 
#5 Re: Help Me ! » What am I doing wrong? » 2008-11-24 13:21:34
Ahh I didn't know that
were the nth roots of unity. Now it makes perfect sense. Thanks!(typo)
#6 Re: Help Me ! » What am I doing wrong? » 2008-11-24 10:02:29
Hi Daniel. I don't get this:
Could you explain it please? :)
#7 Re: Help Me ! » please help me with this problem » 2008-11-19 21:06:13
Hi. You mean you want to simplify it?
#8 Re: Maths Teaching Resources » Free Calculus Tutorial Videos » 2008-10-30 11:17:20
That's awesome! Thank you!!
#9 Re: Help Me ! » Limit » 2008-10-30 11:14:53
(To be honest, I wouldn't be confident about doing that usually. I cheated and evaluated the function for large values of n. It converged to e², and I made the above post with that knowledge.)
I don't know if this is what you mean, but I tried this in maple: seq(limit((1+i/n)^n, n=infinity), i=1..10);
It outputs e^i.
#10 Re: Help Me ! » Limit » 2008-10-30 11:05:13
You can rewrite the numerator as n² - n + 1 + 2n
Oh I missed that, I understand it now! Thank you
#12 Re: Help Me ! » Limit » 2008-10-30 09:15:51
Thanks mathsyperson. I don't understand why the base is approximated by 1 + 2/n. Could you please explain me that part?
#13 Help Me ! » Limit » 2008-10-30 08:02:54
- Nils-Ake
- Replies: 6
Hi! Could you help me calculate this limit?
#14 Re: Help Me ! » Integral » 2008-10-22 05:18:04
Thank you so much
#15 Help Me ! » Integral » 2008-10-22 04:36:54
- Nils-Ake
- Replies: 3
I'm having a hard time with this one. How would you solve it? Maple says the answer is
But I have no clue how to get there.
#16 Re: Help Me ! » diff(1/lnx) » 2008-10-22 04:05:04
Thanks Dude!
#17 Help Me ! » diff(1/lnx) » 2008-10-22 02:56:29
- Nils-Ake
- Replies: 2
Hi. Could someone explain why this is so?
#18 Re: Help Me ! » Area between functions » 2008-04-21 07:08:13
I can't see any flaw in my (now corrected) working, and I trust mathsy too, so hopefully you were right :).
The solution has just been published. We got it right! :)) thank you all for your help.
#19 Re: Help Me ! » Area between functions » 2008-04-20 01:41:09
I have just worked through the correct working, and I get the same thing as you mathsy.
Hm, so you get to the same point. Maybe I wasn't wrong in the end? Thanks a lot for your help :)
#20 Re: Help Me ! » Area between functions » 2008-04-20 01:19:57
Are you sure that what you have done isn't correct?
No, I won't be sure until April 29. But while I was working on this exercise I realized there was a teacher next to me staring at my exam. His face was like "what the hell is this guy doing?". I said to him, "this must wrong..." and then he smiled and walked away. So I assumed my answer was not correct.
#21 Re: Help Me ! » Area between functions » 2008-04-20 00:25:24
No, I don't think so. On his diagram he has shaded the region that I used yellow.
Exactly what Daniel said (from x=3 to +infinity). Sorry if I wasn't clear.
My approach was to calculate the area under both functions so that:
This is what I did:
The integral diverges so the area is undefined.
I guess this would work if I was to calculate the area between f(x) and y=0, but not in this case :\ I don't know how to tell if f(x) converges on g(x).
#23 Re: Help Me ! » Integration » 2008-04-15 06:59:03
Oh well >_< partial fractions again. I'll follow your advice and try to learn it. Thanks.
#24 Re: Help Me ! » Integration » 2008-04-15 06:12:40
wow Dragonshade, that's way too complicated for me, thanks for the answer though :D I've just found out that I'm allowed to use partial fractions, so I guess I'll have to learn how to use them.
Just one more question. Maple says...
It must be obvious but I just can't figure out why.
#25 Re: Help Me ! » Integration » 2008-04-15 04:29:28
Thank you for your answer, Jane I could get the right answer this way, but I'm not supposed to use partial fractions. Is there a way I can do it without using this method?