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प्रश्न
Use the linear approximation to find approximate values of `root(3)(26)`
उत्तर
f(x) = x^(1/3), f(x0) = `(27)^(1/3)` = 2 Δx = – 1
We know that
f(x0 + Δx) = f(x0) + f’(x0) Δx
`(26)^(1/3) = 3 + 1/(3(27)^(2/3)) xx - 1`
= `3 + 1/27 xx - 1`
= `3 - 1/27`
= 3 – 0.370
`(26)^(1/3)` = 2.963
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