Use differentials to approximate the quantity

Question

Use differentials to approximate the quantity

a. √101

b. ⁴√81.6

Answer 1

IF y = x^(1/2) then dy = y₂-y₁ = 1/((2)(x^.5))(x₂-x₁) x₂ = 101 x₁ = 100 then

y2 = 10 + {1/(2)(100^.5)}*(101-100) = 10 + 1/((2)(10))*(101-100) = 10 + .05 = 10.05 = y₂ = 101^(1/2)

(Actual = 10.05)

if y = x^(1/4) then dy = y₂-y₁ = {1/(4*x^.75)}*(x₂-x₁) = {1/(4*3^.75)}*(81.6-81) = .0658

y₂ = 3 + .0658 = 3.0658 (Actual = 3.0055)