## As we know, computers are simple machines that carry out a sequence of very simple steps, albeit very quickly.

### computer science

##### Description

As we know, computers are simple machines that carry out a sequence of very simple steps, albeit very quickly. Unless you have a special-purpose processor, a computer can only compute addition, subtraction, multiplication, and division. If you think about it, you will see that the functions that might interest you when dealing with real or complex numbers can be built up from those four operations. We use many of these functions in nearly every program that we write, so we ought to understand how they are created. If you recall from your calculus class, with some conditions a function f(x) can be represented by its Taylor series expansion near some point f(a): f(x) = f(a)+X∞ k=1 f (k) (a) k! (x−a) k . Note: when you see Σ, you should generally think of a for loop. If you have forgotten (or never taken) calculus, do not despair. Go to a laboratory section for review: the concepts required for this assignment are just derivatives. Since we cannot compute an infinite series, we must be content to calculate a finite number of terms. In general, the more terms that we compute, the more accurate our approximation. For example, if we expand to 10 terms we get:

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