Editing List of real analysis topics (section)

==Fundamental theorems==

*'''[[Monotone convergence theorem]]''' – relates monotonicity with convergence
*'''[[Intermediate value theorem]]''' – states that for each value between the least upper bound and greatest lower bound of the image of a continuous function there is at least one point in its domain that the function maps to that value
*'''[[Rolle's theorem]]''' – essentially states that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative is zero
*'''[[Mean value theorem]]''' – that given an arc of a differentiable curve, there is at least one point on that arc at which the derivative of the curve is equal to the "average" derivative of the arc
*'''[[Taylor's theorem]]''' – gives an approximation of a <math>k</math> times differentiable function around a given point by a <math>k</math>-th order Taylor-polynomial.
*'''[[L'Hôpital's rule]]''' – uses derivatives to help evaluate limits involving indeterminate forms
*'''[[Abel's theorem]]''' – relates the limit of a power series to the sum of its coefficients
*'''[[Lagrange inversion theorem]]''' – gives the Taylor series of the inverse of an analytic function
*'''[[Darboux's theorem (analysis)|Darboux's theorem]]''' – states that all functions that result from the differentiation of other functions have the intermediate value property: the image of an interval is also an interval
*'''[[Heine–Borel theorem]]''' – sometimes used as the defining property of compactness
*'''[[Bolzano–Weierstrass theorem]]''' – states that each bounded sequence in <math>\mathbb{R}^{n}</math> has a convergent subsequence
*'''[[Extreme value theorem]]''' - states that if a function <math>f</math> is continuous in the closed and bounded interval <math>[a,b]</math>, then it must attain a maximum and a minimum