Are you pro-derivatives? If so, well, our politics may clash in the new Problem of the Week, as it is firmly anti-derivative. Only one tool is allowed to solve this pair of problems--the power rule for integration. No u-substitution allowed!
The last Problem of the Week for 2011 is now posted, and it's feeling all festive. Take a journey deep into the cold, barren wastelands of the Northern ice cap and search among the iceburgs to find a certain toymaker's workshop. (In case you need help calculating the derivative of a polar equation.)
With a nod of his head and a wink of his eye, he will promptly ask you to stop trespassing, and for Christmas this year? A restraining order from Santa.
No, this is not how you planned things at all...
Have you ever loved something so deeply, so meaningfully, so completely, so profoundly that it would really irk you if you dropped that thing into a bubbling vat of acid? I have, and so that you may learn from my tragedy, I will share a horrific tale from my past.
Once, on a whim, I spent an entire summer trying to carve a perfect cube from a piece of driftwood on the beach. Don't ask why; this is what all math teachers do during summer break, and if teachers tell you otherwise, they are lying. Look at their hands carefully—they are probably whittling as they lie to you!
Long ago, in the early days of American history, a hearty band of pilgrims landed firmly on Plymouth Rock for two reasons: (1) they sought religious freedom, and (2) they mistimed their jumps, originally aiming for Plymouth Soft Sand and getting a nasty lump on their foreheads as a result. (See last week's My First Cliff Diving Kit for more information, or visit your local library.)
These days we celebrate the seafaring and clumsy spirit of those pilgrims by gathering family together and calcuating derivatives. Enjoy this gravy-soaked chain rule Problem of the Week, and we'll see you in two weeks, after the Thanksgiving holiday.