given data in the image below

by using the above data, please estimate

g(0.5)

using

1. linear interpolation, quadratic interpolation, and cubic interpolation.

Then, calculate the error relative and decide which method gives the best estimation.

Given: X f(x) g(x) h (x) i(x) 0.1 -2.096 0.995 0.100 0.100 0.2 -1.465 0.980 0.199 0.203 0.3 -1.096 0.955 0.296 0.309 0.4 -0.834 0.921 0.389 0.423 0.5 -0.631 0.878 0.479 0.546 0.6 -0.465 0.825 0.565 0.684 0.7 -0.325 0.765 0.644 0.842 0.8 -0.203 0.697 0.717 1.030 0.9 -0.096 0.622 0.783 1.260 1 0.000 0.540 0.841 1.557 by using the above data, please estimate g(0.5) using 1. linear interpolation, quadratic interpolation, and cubic interpolation. Then, calculate the error relative and decide which method gives the best estimation