Comparison of functions O(f) and o(f).

$o (C f) = o (f), C - c o n s t .$

$o (f) + o (f) = o (f) .$

$o (f) o (g) = o (f g) .$

$o (o (f)) = o (f) .$

$O (O (f)) = O (f) .$

$o (O (f)) = o (f) .$

$O (o (f)) = o (f) .$

$o (f) O (f) = o (f) .$

$o (f) + O (f) = O (f) .$

$n \in N, k \in N, n > k .$

$o (x^{n}) + o (x^{k}) = o (x^{k}), x \to 0.$

$o (x^{n}) + o (x^{k}) = o (x^{n}), x \to \infty .$

$O (x^{n}) + O (x^{k}) = O (x^{k}), x \to 0.$

$O (x^{n}) + O (x^{k}) = O (x^{n}), x \to \infty .$

$O (x^{n}) O (x^{k}) = O (x^{n + k}), x \to 0, x \to \infty .$

$f (x) \sim g (x), x \to x_{0} \Leftrightarrow f (x) = g (x) + o (g (x)), x \to x_{0} .$

${\begin{array}{lcl} f (x) \sim f_{1} (x), x \to x_{0}, \\ g (x) \sim g_{1} (x), x \to x_{0}, \\ \exists lim_{x \to x_{0}} \frac{f_{1} (x)}{g_{1} (x)}, \end{array} \Rightarrow lim_{x \to x_{0}} \frac{f (x)}{g (x)} = lim_{x \to x_{0}} \frac{f_{1} (x)}{g_{1} (x)} .$

Tags:

Tables and Formulas

Derivative Table.

Table of Derivatives of Composite Functions.

Table of Higher Order Derivatives.

Table of Integrals

Taylor Series

Comparison of functions O(f) and o(f).

Comparison of functions O(f) and o(f).

Tables and Formulas

Popular posts

Reducing the quadratic form to canonical form.

Calculation of determinants

Logical symbolism. Necessary and sufficient conditions.