a$.$ Write a C program to generate the following table of

$f(x)=x-x^2+\frac{x^6}{100}$

from $x=0$ to $x=4\mathrm{.}0$ with an increment of $0\mathrm{.}1,$ and store the result to a separate

file, table.dat

The following is what the data should look like, while the numbers

given in the table are different from the answer.

b$.$ Transfer the above date file from

omega.uta.edu to a local folder.

Launch gnuplot to read the file, table.dat, and plot the data along with $sinx.$ This

way, you can find out how good approximating $sinx$ by the first three terms of

Taylor series is$.$ The graph should look like