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Definition
More precisely, if a function f is continuous on the closed interval [a, b], where a < b, and differentiable on the open interval (a, b), then there exists a point c in (a, b) such that
f'(c) = {f(b) - f(a)}/{b-a} |
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Definition
A sequence
x_1, x_2, x_3,
of real numbers is called a Cauchy sequence, if for every positive real number ε, there is a positive integer N such that for all natural numbers m, n > N
|x_m - x_n| < E |
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Definition
| We say a function f is continuous at point c, if given any E>0 there exists d>0 such that |x-c| |
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Definition
| There exists a relative extrema on [a,b] at point c if f(x)<=c for all x set of [a,b] or f(x)>=c for all x on interval [a,b] |
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Definition
| The derivative of f(x) at point c is the limit as x->c of f(x)-f(c)/(x-c) |
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| Intermediate Value Theorem |
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Definition
| If f is a continuous function on the domai [a,b] and D is a point such that f(a) < D < f(b). Then there exists a point c, a < c < b such that f(c)=D |
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