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Question
Find the approximate value of (1.999)5.
Solution
(1.999)5 = (2 – 0.001)5
Let x = 2 and Δx = – 0.001
Let y = x5
Differentiating both sides w.r.t, x, we get
`"dy"/"dx"` = 5x4 = 5(2) = 80
Now Δy = `("dy"/"dx") * Δx`
= 80 · (– 0.001)
= – 0.080
∴ (1.999)5 = y + Δy
= x5 – 0.080
= (2)5 – 0.080
= 32 – 0.080
= 31.92
Hence, approximate value of (1.999)5 is 31.92.
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