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A function is y=x^(3). The approximate v...

A function is `y=x^(3)`. The approximate value of the function at `x=2.0001` is possibly (choose the closest answer possible)

A

`8.0006`

B

`8.0008`

C

`8.0012`

D

`8.0015`

Text Solution

Verified by Experts

The correct Answer is:
C
consider `y=x^(3)` at x=2
`y+Deltay=(2.0001)^(3)=(2+0.001)^(3)`
`= (x+Deltax)^(3)`
and `Deltay=3x^(2)Deltax`
`rArr Deltay=3(2)^(2)xx(0.0001)=0.0012`
`:. y=2^(3)+Deltay=8.0012`
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