Numerical calculus based on the analysis of

Intermediate value theorem

Provided f (x) is the interval [a, b] a continuous function, then f (x) takes any of a value between f (a) and f (b).
More strictly,
if c is a number between f (a) and f (b), then there is a number ε (a ≤ ε ≤ b) such that f (ε) = c.

Limit of continuous functions

Provided f (x) in X ₀ continuous function in a neighborhood, and

then

Rolle Mean Value Theorem

Provided f (x) is the interval [a, B] on the continuously differentiable function, and assuming f (a) = f (b), then there is a number c is between a and B, such that f '(c) = 0.

Lagrange mean value theorem

Provided f (x) is the interval [a, B] on the continuously differentiable function, then there exists a number c is between a and B, such that

Taylor Lagrange theorems with remainder term

Let x and x ₀ is a real number, F (x) in the interval [x ₀ , x] (or [x, x ₀ ]) on the k + 1 times continuously differentiable, then x and x ₀ there exists a number c between so that

Second Integral Mean Value Theorem

Provided f (x) is the interval [a, B] continuous function, g (x) is a function of the product, and the change in the number [a, B] on, then there is a number between a and B c, make

to sum up

This paper briefly mentioned intermediate value theorem , the limit of continuous functions , Rolle mean value theorem , Lagrange mean value theorem , the integral value theorem second the content of this five-part, does not elaborate, proof and examples to explain, forget the troubles of higher mathematics review on the books, OK.
These values are based on the analysis, we must not forget ah.