Question

Use an appropriate local linear approximation to estimate the value of √36.03.

Answer 1

Answer:

√36.03 ≈ 6.0025   (approx)

Step-by-step explanation:

Let f(x) = √x.

The derivative is f '(x) = 1 / 2√x.

A linear approximation near x (so for small h) is given by

f '(x) ≈ [ f(x+h) - f(x) ] / h

=> f(x+h) = f(x) + h f '(x)

Putting x = 36 and h = 0.03 gives

√36.03

= f(36 + 0.03)

≈ f(36) + 0.03 f '(36)

= √36 + 0.03 / 2√36

= 6 + 0.03 / 12

= 6 + 0.01 / 4

= 6 + 0.0025

= 6.0025