Prove that $\frac{1}{ 9} < \sqrt {66} - 8 < \frac{1}{ 8}.$
Tags: MVT, approximation, root, using-a-theorem, proof, a--a, t3, c3
This is a hard problem and requires giving students a few hints. I like it because it is not obvious that the MVT can be used to prove the inequality and because it gives students experience in thinking about upper and lower bounds.
– James Epperson 1998-08-09