Compare a function value with nearby left and right evaluations. Each submitted value produces continuity assessment plus the intermediate reasoning.
Continuity at a requires f(a) to exist and equal the common two-sided limit. Numerical checks compare these three quantities.
Reading continuity assessment correctly starts with the mathematical structure described here.
Continuity matters when applying intermediate-value arguments, optimization results, and numerical integration methods. A related application of Continuity Checker is limit estimate.
A numerical pass cannot exclude a specially constructed hole or oscillation below the sample scale.
Reversing the displayed steps offers a quick independent check on this continuity checker result.
For x²+2x at 3, the function value is 15 and nearby values converge to 15.
Evaluate at the point and at symmetric nearby inputs, then inspect the maximum discrepancy.
Start the continuity checker setup by pairing every source number with Function f(x) and Test point. Convert unlike units before typing, and postpone rounding until the displayed continuity assessment is ready to report.
Polynomials remain continuous everywhere, while denominators, roots, logs, and piecewise rules create domain boundaries. Use that direction of change to check the displayed continuity assessment before copying it elsewhere.
When copying the result elsewhere, include its label and any squared, linear, angular, or percentage unit implied by the inputs. That record distinguishes a calculated continuity assessment from an unlabeled number and makes later checking substantially easier.
A limit may exist at a removable hole even when continuity fails because f(a) is missing or reassigned. Keep that boundary in mind when interpreting the numerical result.
For later verification, record Function f(x) and Test point before rounding the continuity assessment. The unrounded working value can feed subsequent steps while the rounded value serves presentation.
The entries defining Continuity are Function f(x) and Test point. Vary one numerical setting while leaving the mathematical problem unchanged. A defensible result should settle as resolution improves. Treat agreement after rounding alone cautiously when the unrounded estimates continue to move.
For this continuity result, a useful record includes the function, relevant bounds, and the numerical convention used here. Those details matter more than the calculator interface and prevent an approximation from being quoted as a symbolic identity.
Value exists, limit exists, and they are equal.
No.
Yes over the reals.