Question

Using differentials, find the approximate value.

1. √0.037

Answer 1

Hi,

Here is your answer,

√0.037 = √(0.040 - 0.003)        x = 0.040 , δx = -.0.003

Let y = √x

 Differentiate with respect to 'x'

 d/dx(y) = d/dx(x)¹/²

dy/dx = 1/2 × x¹/² - 1

dy/dx = 1/2 × x⁻¹/²

dy/dx = 1/2 × 1/2 × 1/x¹/²

dy/dx = 1/2x¹/²

dy = 1/2√x × dx

dy = 1/2√0.040 (-0.003)

 = -0.003/2 × 0.2

 = -0.003/0/4 = -3 × 10⁻³/ 4 × 10⁻¹

 = -3/4 × 10⁻²

 = -3/4 × 1/100

 = -0.75 × 0.001

 dy = -0.0075      { FINAL ANSWER }



Hope it helps you !

Answer 2

Answer:

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