Using differentials, find the approximate values of the following:

(80)1/4

Let us assume that


Also, let x = 81 so that x + Δx = 80


81 + Δx = 80


Δx = –1


On differentiating f(x) with respect to x, we get



We know





When x = 81, we have







Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as



Here, and Δx = 1


Δf = (0.00926)(1)


Δf = 0.00926


Now, we have f(80) = f(81) + Δf




f(80) = 3 – 0.00926


f(80) = 2.99074


Thus, (80)1/4 ≈ 2.99074


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