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Question

Using differentials, find the approximate values of the following:
(ii) (0.009)13

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Solution

Let y=x13dydx=13x23
where, x = 0.008 & Δx=0.001
Now, we know
Δy=(x+Δx)13x13
Δy=(0.008+0.001)13(0.008)13
Δy=(0.009)130.2
(0.009)13=0.2+Δy ...(1)
Now, approximate change in value of y is given by,
Δy(dydx)×Δx
Δy13x23×Δx
Δy13(0.008)23×0.001
Δy0.0010.12
Δy0.00833
From equation (1)
(0.009)130.2+0.00833
(0.009)130.20833

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