استخدام متسلسلات تايلور في تقريب قيم الدوال الأساسية: دراسة لأنواع التقارب وحدود الخطأ (Comprehensive Journal of Science, 2026)
This study examines the use of Taylor series, particularly Maclaurin series, to approximate values of selected elementary functions. It focuses on analyzing the nature of convergence (pointwise and uniform) of partial Taylor polynomials on intervals near the expansion point and on deriving upper bounds for truncation error using the Lagrange remainder formula. The theoretical results are supported by simplified numerical verification, highlighting the relationship between theoretical error bounds and actual computed errors, and clarifying the effect of truncation order and interval selection on approximation accuracy.
Keywords: Taylor series, Maclaurin series, pointwise convergence, uniform convergence, error bound