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Find the approximate values of : f(x)=...

Find the approximate values of :
`f(x)=x^(3)-3x+5" at "x=1.99.`

Text Solution

Verified by Experts

`f(x)=x^(3)-3x+5`
`:.f'(x)=("d")/("dx")(x^(3)-3x+5)`
`=3x^(2)-3xx1+0=3x^(2)-3`
Take a = 2, h = -0.01
Then `f(a)=f(2)=(2)^(3)-3(2)+5`
`=8-6+5=7`
`f'(a)=f'(2)=3(2)^(2)-3=12-3=9`
The formula for approximation is
`f(a+h)=f(a)+h.f'(a)`
`:.f(1.99)=f(2-0.01)=f(2)-(0.01).f'(2)`
`=7-0.01xx9=7-0.09=6.91`
`:.f(1.99)=6.91`.
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