Continuity Calculator

Check if a function is continuous at a point using the three conditions for continuity.

Function & Test Point

f(x) =

Test Point (x = a)

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CONTINUOUS

1. f(a) is definedYES

f(2) = 4

2. lim f(x) existsYES

Left: 3.999996, Right: 4.000004

3. lim f(x) = f(a)YES

Limit = 4, f(a) = 4

Limit exists but either f(a) is undefined or f(a) ≠ limit. Can be "fixed" by redefining f(a).

Left and right limits both exist but are not equal. Function "jumps" at the point.

At least one of the one-sided limits is infinite. Usually involves vertical asymptotes.