Question

find approximate value of 1/square root of 8.08 using differentiation

Answer 1

Answer:

1/√8.08  = 0.336

Step-by-step explanation:

The nearest number to 1/√8.08 whose square root can be taken is 1/√9 so let us consider that x = 1/√9 and δx=dx= - 0.018465

Now consider

y = 1/√x

Differentiating equation with respect to x

dy/dx = -1/2√(x)³

Taking the differential of equation, we get

dy = -1/2√(x)³ dx

Using the values x=1/√4 and dx=0.14, we have

dy = -1/2√(9)³ (0.018)

dy = +0.003

1/√8.08 = y + dy

1/√8.08 = 1/√x + 0.003

1/√8.08  = 1/√9 + 0.003

1/√8.08  = 0.336