Their is another part but not sure how to add, will add in comment section, just need help I don't understand this at all.

Taylor Series Let's say you need to find the square root of 4.7. You pull out your hand calculator (or the Calculator app on your phone), type in v4.7, and you have the answer. But how did the calculator know it? In fact, we take modern computational conveniences for granted. The hand calculator (or the corresponding app) is a fantastic product of engineering; and in this exercise, we're going to apply one of the techniques they use to calculate square roots: Taylor Series. Taylor series allow us to write any differentiable function f(x) as an infinite series of the form f ( z) = f ( a) + f' (a) (x - a) +-1 21 (7 - a)+3(2 - a)3+...+ 1"(1- a)"+... for values of x near x = a. Note that f " (a) represents the n'th derivative of the function f(x) evaluated at x = a. Clearly, the details of a Taylor series expansion depend upon the function involved; for the square root function f (x) = va, it can be shown that: . The Taylor series for f (2:) = va will be an alternating series; that is, the signs of consecutive terms will alternate from positive to negative and back again, with the pattern repeating indefinitely. . If we assume z - a|