Hello everyone! I figured it would be easier if I just uploaded my work pages and posted them instead of trying to type everything out (because I don't know how to use those math tags ) so please find that attached. My calculus final is tomorrow, and I really am just hoping someone can review my work and help me out with a couple of questions I have.
I did everything except #3, 7, and 10.
On #3, can I use a comparison test with an is my original series listed, and with bn being 1/n^2.3? Or do I need to do a limit comparison test, and will bn = 1/n^2.3 work for that? OR did I pick the wrong comparison function? I did try doing the limit comparison test, and I believe I got c=0, so.. yeah I probably did this wrong
On #4, I realize I forgot a negative sign on one of the 1/10. Is it correct, or do I have to write it as a-1/10 < x < a+1/10? Or did I just do it completely wrong?
On #5, I think I may have gotten the wrong taylor series... and for the endpoint x=-8, I I can't use the alternating series test, right? would I be able to use a limit comparison test instead? Actually, upon further review, I'm not even sure what I would compare it to! Maybe... -1/n! ?
On #7, I hate integration by parts, so I skipped over it when I got to that point to make sure I could do everything else. I guess I should ask to confirm, anyway. d/dx [sin (kx)]/k = cos (kx) dx? I know, basic differenatiaon, I'm not very good at cos/sin functions.
And #10, I haven't gotten around to that one yet.
Thanks for the help!