Yearbook Signatures

Posts have been lacking in the last 2 weeks because I've started developing a math note/workbook program for students to more easily take notes or do work on problems, which has been taking up all of my free time.

Pretty much every time I try to write words in a yearbook for a student it comes out completely and utterly cliche. (You're a great student! Have a good summer!  Good luck!)  So, I've decided to stop writing words altogether and usually draw a picture or do some sort of relevant-to-them thing.  Here's a solid work of genius I came up with today:

The answer is pretty worth it, IMHO, so give it a try if you've got some free time!  You can do the harder parts with wolframalpha if you want to cheat. (The integral from ___ of ___, the derivative of ___ at ___, the lim as x approaches ___ of ___)  Sam and Dave, this is a no calculator question for you!

PS- I triple checked the answer would come out right, but I still have a sinking feeling I messed something up.