Functional Continuity Test Calculator

Check left and right limits in seconds quickly. Handle piecewise rules and removable discontinuities clearly. See continuity verdict, tolerances, and detailed numeric steps now.

Calculator

Enter expressions using x. Allowed: + − * / ^, parentheses, and functions like sin, sqrt, ln.

White theme

Test type

Point a

Given f(a)

Used for the continuity check.

Tolerance

Also compute f(a) from expression

Helps compare your input value.

Example data table

Case	Left rule	Right rule	a	f(a)	Expected
Removable gap	sin(x)/x	sin(x)/x	0	1	Continuous
Jump	0	1	0	0	Not continuous
Infinite break	1/x	1/x	0	0	Not continuous

Expressions use radians for trigonometric functions.

Formula used

A function is continuous at x = a when three conditions hold:

f(a) is defined.
The left-hand limit lim(x→a−) f(x) exists.
The right-hand limit lim(x→a+) f(x) exists and equals the left-hand limit, and both equal f(a).

This tool estimates limits numerically by evaluating near a with shrinking step sizes.

How to use this calculator

Choose a test type: piecewise, single rule, or interval scan.
Enter the point a and your chosen value f(a).
Enter expressions using x, like (x^2-1)/(x-1).
Set a tolerance to judge “close enough” equality.
Press Test Continuity to view the verdict and steps.
Use the export buttons to download CSV or PDF.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.