The distance, in feet, a stone drops in seconds is given by . The depth of a hole is to be approximated by dropping a rock and listening for it to hit the bottom. Assume that time measurement is accurate to 1/10ths of a second. Use a linear approximation to estimate an upper bound for the propagated error if the measured time is:
  1. At seconds, the propagated error is at most feet.
  2. At seconds, the propagated error is at most feet.

You can earn partial credit on this problem.