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Thanks bobby I think the symmetry is pretty cool!

**Nils-Ake**- Replies: 8

I have just realized

The finite region is [0,4]:

Expand f(x):

Integrate:

*edit: added graph*

**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?

Ahh I didn't know that

were the nth roots of unity. Now it makes perfect sense. Thanks!(typo)

Hi Daniel. I don't get this:

Could you explain it please? :)

Hi. You mean you want to simplify it?

That's awesome! Thank you!!

mathsyperson wrote:

(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.

You can rewrite the numerator as n² - n + 1 + 2n

Oh I missed that, I understand it now! Thank you

**Nils-Ake**- Replies: 6

Hi! Could you help me calculate this limit?

Thank you so much

**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.

Thanks Dude!

**Nils-Ake**- Replies: 2

Hi. Could someone explain why this is so?

Daniel123 wrote:

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.

Daniel123 wrote:

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 :)

Daniel123 wrote:

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.

Daniel123 wrote:

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).

Oh well >_< partial fractions again. I'll follow your advice and try to learn it. Thanks.

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.