Question

Use a linear approximation (or differentials) to estimate the given number:
1/4.002

Answer 1

Given that 1/4 = 0.25

Set f(x) = 1/x
Then f'(x) = -1/x^2

Thus 1/4.002 = f(4.002) ≈ f(4) + f'(4) * (4.002 - 4) = 1/4 - 1/4^2 * 0.002 = 0.25 - 0.000125 = 0.2499