help with a calculus problem: toothpaste
what are some different ways you have tried to get the last bit of toothpaste out of the bottle? I'm supposed to think of ideas but I've only thought of three, and yes this actually ties into a calculus problem (we have to mathematically find the volume of toothpaste that is inside a wrapped up toothpaste container given a function that represents the edges of the toothpaste container ).
the three I've come up with:
-squeeze really hard
-put a key at the bottom and roll the tube up to squeeze the last bit out
-cut the toothpaste bottle open to scrape it out