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Question
Use the linear approximation to find approximate values of `root(4)(15)`
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Solution
`root(4)(15) = (15)^(1/4)`
f(x) = `x^(1/4), f(x0) = `(16)^(1/4)` = 2
We know that
f(x0 + Δx) = f(x0) + f’(x0) Δx
`(15)^(1/4) = 2 + 1/(4x^(1/4)) (- 1)`
= `2 + 1/(4(16)^(3/4)) (- 1)`
= `2 + 1/(4 xx 8) (- 1)`
= `2 - 1/32`
= 2 – 0.03125
`(15)^(1/4)` = 1.96875
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