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# For writer #1170 - Essay Example

Summary
Definition of functional limit: - Lim/x->a (f(x) = L if and only if for every > 0 there exists a real positive >0 such that the following holds | f(x) - L | < whenever | x - a| < . Given that for the real functions f and g, f(x) F and g(x) G as x a, For convenience lets alias f(x) to f and g(x) to g.

## Extract of sample "For writer #1170"

Download file to see previous pages for this 'e' then it obviously holds for larger numbers also. (We have deliberately added 1 on the rhs, taking into account the possibility of both F, G being = 0. so we need to make rhs some strictly positive quantity).

See that (4) e. (2(|F| +|G|) + 1) and this we need it to be < , that is we need
e < / (2(|F| +|G|) +1).

So the procedure is to start with e = minimum {/ (2(|F| +|G|) +1), (|F| +|G| +1)} which is
clearly > 0 and so this has its 1, 2 satisfying our (1) and choose to be the minimum of
these two.

The steps in order now are:-
| f.g -F.G| e.(e + |F| +|G| ) by (4). and e / (2(|F| +|G|) +1), so
[/ (2(|F| +|G|) +1)]. (e + |F| +|G|) and again e is also (|F| +|G| +1), so
[/ (2(|F| +|G|) +1)]. (2(|F| +|G|) +1)
= , everything holding for our as chosen.
Thus for any given > 0 we are able to find out a satisfying the limit condition, f.g ...Download file to see next pagesRead More
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