In: Advanced Math
Use the Mean-Value Theorem to prove that 30/203 < √ 103 − 10 < 3 /20 .
Solution: Let (where
) be any two
distinct points of
, then by
Lagrange's mean value theorem, we get
or
Let
, then for
so that
.
Then from above, we can write
--------------------------------(a)
Again, for
so that
. Then from
above, we can write
........................................(b)
Combining (a) and (b), we obtained the required result