Analysis. Using a calculator, the value of 9.1 9.1 to four decimal places is 3.0166. The value given by the linear approximation, 3.0167, is very close to the value obtained with a calculator, so it appears that using this linear approximation is a good way to estimate x, x, at least for x x near 9. 9. At the same time, it may seem odd to use a linear approximation when we can just push a few.