The same in a relative way

And here, finally, is question 8.

This question went really well. It was the one I worried about most and studied for right up to the minute when I went down to the exam room. In the event it went like a dream - it followed the process we'd learned in class exactly without any tricksy deviations, and my memory didn't fail me at the moment of crisis. I know that my process was correct, regardless of mechanical errors, and that's the most important thing.

The hint at the bottom surprised me, though. Firstly that we got a hint at all [this is 300-level!], but secondly - why does it give the formulae for a sine series, when I quite clearly got a cosine series out of my workings? Unless I can be bothered waiting two months to get the paper back, I'll never know whether it was me or the hint that was in error.

Didn't quite finish part (e), as you can tell. I started it so near to the end of the exam that I kept pausing after each line of working to see if we would be stopped yet. In the end I did manage to lay down my pen right in the middle of a line - so the markers can see that the last line on the page wasn't my intended final answer. I did know that it could be simplified further sir, I just didn't have time to do it.

The results should be out any day now. Or sometime within the next week. Or two...