Limit of a function

Point to which functions converge in analysis x {\displaystyle x} sin ⁡ x x {\displaystyle {\frac {\sin x}{x}}} 1 0.841471... 0.1 0.998334... 0.01 0.999983... Although the function ⁠ sin ⁡ x x {\displaystyle {\tfrac {\sin x}{x}}} ⁠ is not defined at zero, as x becomes closer and closer to zero, ⁠ sin ⁡ x x {\displaystyle {\tfrac {\sin x}{x}}} ⁠ becomes arbitrarily close to 1. In other words, the limit of ⁠ sin ⁡ x x , {\displaystyle {\tfrac {\sin x}{x}},} ⁠ as x approaches zero, equals 1. Part of a series of articles aboutCalculus ∫ a b f ′ ( t ) d t = f ( b ) − f ( a ) {\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)} Fundamental theorem Limits Continuity Rolle's theorem Mean value theorem Inverse function theorem Differential Definitions Derivative (generalizations) Differential infinitesimal of a function total Concepts Differentiation notation Second derivative Implicit differentiation Logarithmic differentiation Related rates Taylor's theorem Rules and identities Sum Product Chain Power Quotient L'Hôpital's rule Inverse General Leibniz Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Ant