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If y=x^(4)-6x^(3)+13x^(2)-11x+4, then ap...

If `y=x^(4)-6x^(3)+13x^(2)-11x+4`, then approximate valueof y when `x=2.01` is

A

`2.12`

B

`2.01`

C

`2.31`

D

`2.21`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `x=2.01, a=2, h=0.01`
`f(x)=x^(4)-6x^(3)+13x^(2)-11x+4`
Now `f(2)=16-48+52-22+4=24-22=2`
and `f'(x)=4x^(3)-18x^(2)+26x-11`
`:.f'(2)=32-72+52-11=84-83=1`
Now `f(a+h)=f(2)+hf'(2)`
`impliesf(2+0.01)=2+(0.01)1=2.01`
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