Calculus
Lab: sequences and series of functions
Follow fₙ or partial sum Sₙ, compare the limit and distinguish point error from global error. A grid maximum is not a whole-domain guarantee.
Model, domain and analytical conclusion
One second per index: each step increases n by 1. The blue point stays fixed; the red point may move. Finite animations illustrate formulas, not prove limits.
Functions and limit
Fixed point x* lies outside the zoomed window, but its value is still listed below.
Errors and values at the current step
Error as n changes
Value table
Eₙ and bounds come from article formulas, not grid searches. Values use floating point: rounding matters near ε and for tiny remainders. Oscillations are sampled and zoom redistributes the 21 nodes within the window. Theoretical truncation error excludes computer rounding. Interchanging limits with integrals or derivatives requires the article’s assumptions.