Consider the function: f(x) = – 0.78 – 0.25 – 0.45 – 0.25x + 1.2 . (a) develop 2-, 4-, and 6-term taylor series expansions, g(x), about x0 = 0. (b) plot the exact function, f(x), as well as each of the three taylor series expansions over the interval [0,1] using a plotting increment equal to at least 0.05. (c) plot the actual error, e(x) = f(x) – g(x) and the estimated error, e(x), which can be estimated by the leading- order truncated term for each of the three taylor series expansions. plot these error measures against the distance about the expansion point on log-log axes. (d) how do the errors generally behave when the distance from the expansion point becomes larger? (e) why is the 6-term expansion exact (i. e. both the estimated error and the actual error terms are equal to zero)?