Calculus
Lab: multivariable limits and continuity
Compare straight and curved paths approaching the origin. Two disagreeing paths disprove a limit; agreeing paths do not prove it. For convergent cases also use an analytical ε–δ bound.
Domain, limit and point value
A guarantee on the whole disk, not just paths
One step per second. Tables and points update; t=0 is never evaluated. Parameter t is not necessarily distance r.
Blue: A. Orange: B. Green: δ-disk. The value-plot band is L±ε; without a limit, 0 is only a graphical reference.
Surface and paths
Paths in the plane and δ-disk
One or more points lie outside the plotted window; numerical values remain valid.
Values along both paths
Value table
Plots and values are floating-point samples, not proofs. The 3D mesh can miss narrow ridges and fast oscillations; paths use the formula directly. Zoom and vertical scaling affect the view, not the domain. Stated path limits and ε–δ bounds are analytical. Assigning an origin value does not change the limit.