Use differentials to approximate the quantity

Question

Use differentials to approximate the quantity.

Square root of 80.7

Answer 1

Let consider function f(x) = x^1/2; at x₀ = 81; f(x₀) = f(81) = 81^1/2 = 9. At x = 80.7 we have dx = Δx = x - x₀ = - .3;

f(x) = f(x₀) + Δf(x) ≈ f(x₀) + df(x) = f(x₀) + 1/2x₀^-1/2dx = · 9 + 1/2(81)^-1/2·(- .3) = 9 - 0.3/18 = 9 - 1/60 ≈ 8.9833

Answer: 80.7^1/2 ≈ 8.9833