Use the Mean-Value Theorem to prove that 30/203 < √ 103 − 10 < 3 /20...

Use the Mean-Value Theorem to prove that 30/203 < √ 103 − 10 < 3 /20 .

Expert Solution

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

Colby Messinger answered 2 years ago

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