ANSWERS TO THE CALCULUS FINAL
               by A Concerned and Resourceful Student

1)  The Derivative Is Our Friend.

2)  The Derivative Is Very Useful.   (We know this because people use it
all the time.)

3)  The Derivative Is Very Old.   (This result can be obtained by looking
at how long the derivative has been around, and then subtracting from Now.)

4)  The Derivative was invented by two guys, one of whom was Newton, who
also makes a mighty nice cookie.

5)  a:  The limit of the sum is the sum of the limits.
    b:  The limit of the product is the product of the limits.
    c:  The needs of the many outweigh the needs of the few.  Or the one.

6)  The Derivative is Not Our Foe.   (This result is easily proved by
assuming that the derivative is our foe, then using #1 above to obtain a
contradiction.)

7)  ...NOW, multiply by the derivative of what's INSIDE the brackets...
with respect to x...

8)  When in doubt, refer to #1.

Extra Credit:

9)  1812.  (Trick question.  Every Calculus final requires at least one
problem with an actual numeric solution.  Students who forget this are
often tempted to put "Ulysses S. Grant" as the answer here.)

10)  Write a question appropriate for a Calculus final, then answer it.
Write a question appropriate for a Calculus final, then answer it.