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The approximate value of (80.7)^(1//4) i...

The approximate value of `(80.7)^(1//4)` is

A

`2.99822`

B

`2.96600`

C

`2.95399`

D

`2.99722`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `f(x)=x^(1/4)`, then `f(x+h)=(x+h)^(1/4)`
`:.f'(x)=1/4x^(1/4-1)=1/4x^(-3/4)`
Let `a=81h,=-0.3`
`:.f(a+h)~~hf'(a)+f(a)`
`=-0.3 . 1/4 (81)^(-3/4)+(81)^(1/4)=-0.3/4 . 3^(-3)+3`
`=-0.3/105+3=-0.3/108+3=2.99722`
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