Mathematics

Limits \[ \lim_{x \to c} f(x) = L \] Discontinuity * Removable Discontinuity * Jump Discontinuity * Essential Discontinuity Derivatives

Category A category is a collection of objects that are linked by arrows. Morphisms Universal Construction Functor A functor is a map between categories. Definition Let C and D be categories. A functor F from C to D is a mapping that: * associates to each object \(X\) in C an

* Group * Field * Ring * Category

A function \(f\) from a set \(D\) to a set \(Y\) is a rule that assigns a unique value \(f(x)\) in \(Y\) to each \(x\) in \(D\). The set \(D\) of all possible input values is called the domain of the function. The set of all output values of

When \(a \ne 0\) , there are two solutions to \(ax^2 + bx + c = 0\) and they are \[x = {-b \pm \sqrt{b^2-4ac} \over 2a}.\] Discriminant: \(D = b^2-4ac\) If \(\alpha\) and \(\beta\) are the roots of quadratic equation (\(ax^2 + bx + c = 0\)), then: * \(\alpha + \beta = -{b \over