Limit of a function

Approach a point from the left and right, then watch the function values move toward a common value — or fail to do so.

Choose a function

x-min

x-max

Target point a = 1 Distance h = 1.0000 Animation speed

f(x) left: x = a − h right: x = a + h x = a

Left-side value

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Right-side value

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Function value at a

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Observation

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Classroom idea: Pause the marker and ask students: "Do the left-hand and right-hand y-values approach the same number?" If yes, discuss the limit. If not, ask whether the problem is a jump, asymptote, or oscillation.