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- Haught
- Important definitions and theorems

Dawn H.

The epsilon-delta definition of the limit

The limit of f(x) as x approaches a equals L if for every epsilon greater than 0 there is a delta greater than 0 such that if 0 < |x-a| < delta, then |f(x)-L| < epsilon

Definition of Continuous

1) f(c) is defined

2) lim_{x->c}f(x)=f(c)

3) lim_{x->c}f(x) exists

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Then if *f*(*c*_{1}) < M < *f*(*c*_{2}),

there is a number *c*_{2} in (c_{1}* , c*_{3}),

such that *f*(*c*_{2}) = M .

The Derivative of f(x)

f'(x)=

limit as h approaches 0 of (f(x + h) - f(x))/h

The Extreme Value Theorem

If f is continuous on an interval [a,b], then f has an absolute max value f(c) and absolute min value f(d) at some number c and d on the closed interval [a,b]

(Check where f'(x)= 0 and the ends of the interval)

f'(c)= (f(b)-f(a))⁄(b-a)

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