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  2. Taylor's theorem - Wikipedia

    en.wikipedia.org/wiki/Taylor's_theorem

    In calculus, Taylor's theorem gives an approximation of a -times differentiable function around a given point by a polynomial of degree , called the -th-order Taylor polynomial. For a smooth function , the Taylor polynomial is the truncation at the order k {\textstyle k} of the Taylor series of the function.

  3. Convergence tests - Wikipedia

    en.wikipedia.org/wiki/Convergence_tests

    Mean value theorem; Inverse function theorem; ... Taylor; Convergence tests; Summand limit (term test) ... This is also known as the nth-term test, ...

  4. List of calculus topics - Wikipedia

    en.wikipedia.org/wiki/List_of_calculus_topics

    First derivative test; Second derivative test; Extreme value theorem; Differential equation; Differential operator; Newton's method; Taylor's theorem; L'Hôpital's rule; General Leibniz rule; Mean value theorem; Logarithmic derivative; Differential (calculus) Related rates; Regiomontanus' angle maximization problem; Rolle's theorem

  5. nth-term test - Wikipedia

    en.wikipedia.org/wiki/Nth-term_test

    Mean value theorem; Inverse function theorem; ... Taylor's theorem; Rules and identities ... In the case of p-adic analysis the term test is a necessary and ...

  6. Root test - Wikipedia

    en.wikipedia.org/wiki/Root_test

    Mean value theorem; Inverse function theorem; ... the root test is a criterion for the convergence ... From Taylor's expansion applied to the right-hand side, ...

  7. Delta method - Wikipedia

    en.wikipedia.org/wiki/Delta_method

    Demonstration of this result is fairly straightforward under the assumption that () is differentiable near the neighborhood of and ′ is continuous at with ′ ().To begin, we use the mean value theorem (i.e.: the first order approximation of a Taylor series using Taylor's theorem):

  8. Derivative test - Wikipedia

    en.wikipedia.org/wiki/Derivative_test

    The first-derivative test depends on the "increasing–decreasing test", which is itself ultimately a consequence of the mean value theorem. It is a direct consequence of the way the derivative is defined and its connection to decrease and increase of a function locally, combined with the previous section.

  9. Mean value theorem - Wikipedia

    en.wikipedia.org/wiki/Mean_value_theorem

    Cauchy's mean value theorem, also known as the extended mean value theorem, is a generalization of the mean value theorem. [ 6 ] [ 7 ] It states: if the functions f {\displaystyle f} and g {\displaystyle g} are both continuous on the closed interval [ a , b ] {\displaystyle [a,b]} and differentiable on the open interval ( a , b ) {\displaystyle ...