Math Is Fun Forum

I got my quiz back and my professor gave me full points. Remember that my final answer consisted of saying "this series diverges absolutely". I did know that if a series diverges absolutely you can't imply that it diverges conditionally.

Anyways, the solution he gave on the board was:

Since the limit is not equal to 0 then it diverges. So basically he used the Divergence Test which says that if the limit of the series is not 0 then the series diverges. I did use this test and I saw that it gave me 1 (which is probably why he gave me the full points) but I didnt draw any conclusions because I took the limit of just k/(k+1) and thats not the actual series. The actual series is alternating.

So from his conclusions and his answer on the board you can deduce this:

But isnt this wrong? b_k is the absolute of a_k so by finding that the limit of b_k is not equal to 0, your actually finding that b_k diverges. But b_k is the absolute of a_k and if a series diverges absolutely it doesnt imply it diverges conditionally.

So my professor is wrong?

Please tell me if you can't follow my reasoning as im very intrigued by this.

I've never understood it. Like, it just seems something I would had done when I was 8yrs old and not now...Dont know.

What you have to realize is that in the initial problem you said to rotate around the x-axis which is the same as rotating around y=0. In which case we setup the integral as dy. If you now rotate around x=1 then the integral changes to dx and it changes completely.

You cant rotate it around y=2. It cuts the graph. You would have to rotate it around the x-axis (y=0) or around y = negative

No problem. Pleasure to help you.

Thanks Dragonshade for confirming I was right.

Its just algebra. Nothing to do with calculus.

Do you see it now?

Your right. My bad.

So:

So the integral that we setup is in this form:

To be honest, im not sure myself I did it right. Feel free to find any errors on my part because I want to know myself if I did it right. This solids of revolutions were always tricky

The formula to find the volume of a solid using the shell method is this:

So to set up your integral it would be like this:

Yes please. I would appreciate it.

Meh.

I was just playing with my stupid engine and the game went on like this:

e4 d6
f4 Na6
Nf3 Rb8
Bxa6 Ra8

Even if my evaluation function is as simple as you can get, when its searching, guiding itself by my eval function, why did it find Ra8 to be "better" than bxa6? If I understand this alpha-beta searching, the search function is supposed to evaluate every single position, bxa6 is supposed to give a higher score than Ra8 since with any other move that isnt bxa6 the score goes down by 3...

Hmm.