limitlari

Limitlari is the Turkish term that appears in mathematical contexts to refer to limits in plural form, or more broadly to the concept of limits as used in calculus and analysis. The idea of a limit describes the value that a function or a sequence approaches as its input or index approaches a specified point or infinity.

For a real-valued function f defined near a (excluding a itself), lim x→a f(x) = L means that as x gets arbitrarily close to a (but not equal to a), the function values f(x) get arbitrarily close to L. This is often formalized using the epsilon-delta definition: for every epsilon > 0 there exists delta > 0 such that 0 < |x − a| < delta implies |f(x) − L| < epsilon. For sequences, lim n→∞ a_n = L means that for every epsilon > 0 there exists N such that n ≥ N implies |a_n − L| < epsilon. One-sided limits, written lim x→a+ and lim x→a−, describe approach from the right or left. Limits at infinity describe behavior as the input grows without bound.

Limit laws summarize how limits behave under basic operations: the limit of a sum is the sum of the limits, the limit of a product is the product of the limits, and so on, provided the individual limits exist. Limits help formalize continuity, derivatives, integrals, and series convergence.

In Turkish mathematics, limitleri (the plural form) appears in discussions of multiple limits or when referring to the limits of several functions. If a limit does not exist, it may be due to oscillation, divergence, or approaching different values from different directions.